Open App

Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Assertion & Reason Type Questions: Polynomials

Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials

Q: 1. What is a polynomial in mathematics?

Ans. A polynomial is a mathematical expression that consists of variables raised to whole number powers and coefficients. It takes the form of a sum of terms, where each term is a product of a coefficient and a variable raised to a non-negative integer exponent. For example, the expression 3x² + 2x - 5 is a polynomial.

Q: 2. How do you classify polynomials based on their degree?

Ans. Polynomials can be classified by their degree, which is determined by the highest exponent of the variable in the expression. A polynomial of degree 0 is called a constant, degree 1 is linear, degree 2 is quadratic, degree 3 is cubic, degree 4 is quartic, and degree 5 is quintic. For instance, in the polynomial 4x³ + 2x + 1, the degree is 3.

Q: 3. What are the different operations that can be performed on polynomials?

Ans. The primary operations that can be performed on polynomials include addition, subtraction, multiplication, and division. Addition and subtraction involve combining like terms, while multiplication involves distributing each term in one polynomial to each term in the other. Division can be more complex and often involves polynomial long division.

Q: 4. Can you explain the concept of the roots of polynomials?

Ans. The roots of a polynomial are the values of the variable that make the polynomial equal to zero. For example, if P(x) = 0, then x is a root of the polynomial P. The Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n roots, counting multiplicities and complex roots.

Q: 5. What is the significance of the Remainder Theorem in relation to polynomials?

Ans. The Remainder Theorem states that when a polynomial f(x) is divided by a linear divisor of the form (x - c), the remainder is equal to f(c). This theorem helps in evaluating polynomials at specific points and aids in factoring polynomials, as it indicates whether a particular value is a root of the polynomial.

Q1: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : x² + 4x + 5 has two real zeroes.
Reason : A quadratic polynomial can have at the most two zeroes.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: d
p(x) = 0 ⇒ x² + 4x + 5 = 0
Discriminant, D = b² – 4ac
= 4² – 4 x 1 x 5
= 16 – 20 = – 4 < 0
Therefore, no real zeroes are there.

Q2: Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If the sum of the zeroes of the quadratic polynomial x²- 2kx + 8 is 2 then value of k is 1.
Reason: Sum of zeroes of a quadratic polynomial ax²+ bx + c is - b/a
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: a
Assertion (A): If the sum of the zeroes of the quadratic polynomial x² - 2kx + 8 is 2, then the value of
k is 1.
Reason (R): The sum of the zeroes of a quadratic polynomial ax² + bx + c is - (b/a).
Let's evaluate these statements:
For a quadratic equation ax2 + bx + c, the sum of the zeroes is given by - (b/a).
Given the quadratic polynomial x² - 2kx + 8, if the sum of the zeroes is 2, then we have:
- (- 2k / 1) = 2
2k = 2
k = 1
So, both assertion (A) and reason (R) are true, and reason (R) correctly explains assertion (A).
Therefore, the correct choice is:
1. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Q3: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion (A): If the zeroes of the quadratic polynomial (k – 1) x² + kx + 1 is – 3, then the value of k is 4/3.
Reason (R): If – 1 is a zero of the polynomial p(x) = kx² – 4x + k, then the value of k is –2.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: b
In case of assertion:
Let p(x) = (k – 1)x² + kx + 1
As –3 is a zero of p(x), then p (−3) = 0
⇒ (k – 1) (−3)² + k (−3) + 1 = 0
⇒ 9k – 9 – 3k + 1 = 0
⇒ 9k – 3k = +9 – 1
⇒ 6k = 8
⇒ k = 4/3
∴ Given statement is correct.
In case of reason:
Since, – 1 is a zero of the polynomial and p(x) = kx² – 4x + k, then p (–1) = 0
∴ k (–1)² – 4 (–1) + k = 0
⇒ k + 4 + k = 0
⇒ 2k + 4 = 0
⇒ 2k = – 4
Hence, k = – 2
∴ Given statement is correct.
Thus, both assertion and reason are correct but reason is not the correct explanation for assertion.

Q4: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If one zero of poly-nominal p(x) = (k² + 4)x²+ 13x + 4k is reciprocal of other, then k = 2.
Reason : If (x - α) is a factor of p(x), then p(α) = 0 i.e. α is a zero of p(x).
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: b
Reason is true.Let α, 1/α be the zeroes of p(x), then
k² - 4k + 4 = 0
(k - 2)² = 0
k = 2 Assertion is true Since, Reason is not correct for Assertion.

Q5: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : (2 - √3) is one zero of the quadratic polynomial then other zero will be (2 + √3).
Reason : Irrational zeros (roots) always occurs in pairs.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: a
As irrational roots/zeros always occurs in pairs therefore, when one zero is (2 - √3) then other will be (2 + √3). So, both A and R are correct and R explains A.

Q6: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : The graph y = f(x) is shown in figure, for the polynomial f(x). The number of zeros of f(x) is 3.

Reason : The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: c
As the number of zeroes of polynomial f(x) is the number of points at which f(x) cuts (intersects) the x –axis and number of zero in the given figure is 3.
So A is correct but R is not correct.

Q7: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : P(x) = 14x³ - 2x² + 8x⁴ + 7x - 8 is a polynomial of degree 3.
Reason : The highest power of x in the polynomial p(x) is the degree of the polynomial.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: d
The highest power of x in the polynomial p(x)= 14x³ - 2x² + 8x⁴ + 7x - 8x is 4.
Degree of p(x) is 4. So, A is incorrect but R is correct.

Q8: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : The graph y = f(x) is shown in figure, for the polynomial f (x). The number of zeros of f(x) is 3.
Reason : The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: c
As the number of zeroes of polynomial f(x) is the number of points at which f(x) cuts (intersects) the x –axis and number of zero in the given figure is 3.So A is correct but R is not correct.

Q9: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : Zeroes of f(x) = x² - 4x - 5 are 5, - 1
Reason : The polynomial whose zeroes are 2 + √3, 2 - √3 is x² - 4x + 7.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: c
Zeroes of f(x) = x² − 4x − 5 are obtained by solving:
x² − 4x − 5 = 0, which implies
x² − 5x + x − 5 = 0 or, x(x − 5) + 1(x − 5) = 0
which means x = 5 or x = −1
Thus the assertion is correct.
However, the reason is incorrect.
The numbers given are not the zeroes of x² − 4x + 7

Q10: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : x³ + x has only one real zero.
Reason : A polynomial of nth degree must have n real zeroes.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: c
Reason is false [a polynomial of n^th degree has at most x zeroes.] Again, x³ + x = x(x² + 1)
which has only one real zero (x = 0)
[x² + 1 ≠ 0 for all x ε R]
Assertion is true.

Q11: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If one zero of poly-nominal p(x) = (k² + 4)x² + 13x + 4k is reciprocal of other, then k = 2.
Reason : If (x – a) is a factor of p(x), then p(a) = 0 i.e. a is a zero of p(x).
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: b
Let α, 1/α be the zeroes of p(x) then we have
Product of Zeroes
= a x (1/a) = 4k / (k² + 4) = 1
⇒ k² – 4k + 4 = 0
⇒ (k – 2)² = 0 ⇒ k = 2

Q12: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: Degree of a zero polynomial is not defined.
Reason: Degree of a non-zero constant polynomial is 0
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: b
We know that, the constant polynomial 0 is called a zero polynomial. The degree of a zero polynomial is not defined.So, Assertion is true. Now, the degree of a non-zero constant polynomial is zero. So, Reason is true.

Q13: Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If the product of the zeroes of the quadratic polynomial x²+ 3x + 5k is -10 then value of k is -2.
Reason: Sum of zeroes of a quadratic polynomial ax²+ bx + c is -b/a
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: b
Both the assertion and the reason are true, but the reason provided is related to the sum of the zeroes, not their product. The correct explanation involves the formula for the product of the zeroes of a quadratic polynomial, c/a, which would lead to 5k/−10, hence determining the value of k.

Q14: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The sum and product of the zeros of a quadratic polynomial are -1/4 and 1/4 respectively.
Then the quadratic polynomial is 4x² + x + 1.
Reason : The quadratic polynomial whose sum and product of zeros are given is x²-(sum of zeros). x + product of zeros.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: a
Sum of zeros = -1/4 and product of zeros = 1/4
Quadratic polynomial be 4x² + x + 1. So, both A and R are correct and R explains A.

Q15: Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : x² + 7x + 12 has no real zeroes.
Reason : A quadratic polynomial can have at the most two zeroes.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Ans: d
x² + 7x + 12 = 0⇒ x² + 4x + 3x + 12 = 0
⇒ x(x + 4) + 3(x + 4) = 0
⇒ (x + 4) (x + 3) = 0
⇒ (x + 4) = 0 or (x + 3) = 0
⇒ x = −4 or x = −3
Therefore, x² + 7x + 12 has two real zeroes.

The document Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials is a part of the Class 10 Course Mathematics (Maths) Class 10.

All you need of Class 10 at this link: Class 10

	Mathematics (Maths) Class 10 129 videos\|736 docs\|84 tests

Mathematics (Maths) Class 10

129 videos|736 docs|84 tests

Join Course for Free

FAQs on Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials

1. What is a polynomial in mathematics?

Ans. A polynomial is a mathematical expression that consists of variables raised to whole number powers and coefficients. It takes the form of a sum of terms, where each term is a product of a coefficient and a variable raised to a non-negative integer exponent. For example, the expression 3x² + 2x - 5 is a polynomial.

2. How do you classify polynomials based on their degree?

Ans. Polynomials can be classified by their degree, which is determined by the highest exponent of the variable in the expression. A polynomial of degree 0 is called a constant, degree 1 is linear, degree 2 is quadratic, degree 3 is cubic, degree 4 is quartic, and degree 5 is quintic. For instance, in the polynomial 4x³ + 2x + 1, the degree is 3.

3. What are the different operations that can be performed on polynomials?

Ans. The primary operations that can be performed on polynomials include addition, subtraction, multiplication, and division. Addition and subtraction involve combining like terms, while multiplication involves distributing each term in one polynomial to each term in the other. Division can be more complex and often involves polynomial long division.

4. Can you explain the concept of the roots of polynomials?

Ans. The roots of a polynomial are the values of the variable that make the polynomial equal to zero. For example, if P(x) = 0, then x is a root of the polynomial P. The Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n roots, counting multiplicities and complex roots.

5. What is the significance of the Remainder Theorem in relation to polynomials?

Ans. The Remainder Theorem states that when a polynomial f(x) is divided by a linear divisor of the form (x - c), the remainder is equal to f(c). This theorem helps in evaluating polynomials at specific points and aids in factoring polynomials, as it indicates whether a particular value is a root of the polynomial.

About this Document

2.5K Views

4.80/5 Rating

Sep 20, 2025 Last updated

Related Exams

Class 10 Grade 10

Document Description: Assertion & Reason Type Questions: Polynomials for Class 10 2025 is part of Mathematics (Maths) Class 10 preparation. The notes and questions for Assertion & Reason Type Questions: Polynomials have been prepared according to the Class 10 exam syllabus. Information about Assertion & Reason Type Questions: Polynomials covers topics like and Assertion & Reason Type Questions: Polynomials Example, for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Assertion & Reason Type Questions: Polynomials.

Introduction of Assertion & Reason Type Questions: Polynomials in English is available as part of our Mathematics (Maths) Class 10 for Class 10 & Assertion & Reason Type Questions: Polynomials in Hindi for Mathematics (Maths) Class 10 course. Download more important topics related with notes, lectures and mock test series for Class 10 Exam by signing up for free. Class 10: Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials

Description

Full syllabus notes, lecture & questions for Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials - Class 10 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 10 | Best notes, free PDF download

Information about Assertion & Reason Type Questions: Polynomials

In this doc you can find the meaning of Assertion & Reason Type Questions: Polynomials defined & explained in the simplest way possible. Besides explaining types of Assertion & Reason Type Questions: Polynomials theory, EduRev gives you an ample number of questions to practice Assertion & Reason Type Questions: Polynomials tests, examples and also practice Class 10 tests

	Mathematics (Maths) Class 10 129 videos\|736 docs\|84 tests

Mathematics (Maths) Class 10

129 videos|736 docs|84 tests

Join Course for Free

Download as PDF

Explore Courses for Class 10 exam

Exam

Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials

video lectures

Free

Viva Questions

shortcuts and tricks

Objective type Questions

Summary

Previous Year Questions with Solutions

ppt

practice quizzes

Important questions

Sample Paper

pdf

Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials

past year papers

Semester Notes

Extra Questions

study material

Class 10 Maths Chapter 2 Assertion and Reason Questions - Polynomials

mock tests for examination

MCQs

;

Additional Information about Assertion & Reason Type Questions: Polynomials for Class 10 Preparation

Assertion & Reason Type Questions: Polynomials Free PDF Download

The Assertion & Reason Type Questions: Polynomials is an invaluable resource that delves deep into the core of the Class 10 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the Assertion & Reason Type Questions: Polynomials now and kickstart your journey towards success in the Class 10 exam.

Importance of Assertion & Reason Type Questions: Polynomials

The importance of Assertion & Reason Type Questions: Polynomials cannot be overstated, especially for Class 10 aspirants. This document holds the key to success in the Class 10 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Assertion & Reason Type Questions: Polynomials Notes

Assertion & Reason Type Questions: Polynomials Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Assertion & Reason Type Questions: Polynomials. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Assertion & Reason Type Questions: Polynomials Notes on EduRev are your ultimate resource for success.

Assertion & Reason Type Questions: Polynomials Class 10

The "Assertion & Reason Type Questions: Polynomials Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Assertion & Reason Type Questions: Polynomials on the App

Students of Class 10 can study Assertion & Reason Type Questions: Polynomials alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Assertion & Reason Type Questions: Polynomials, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Assertion & Reason Type Questions: Polynomials is prepared as per the latest Class 10 syllabus.

Education Revolution