All Courses
Get the App Signup / Login
Sign in Open App
Class 9 Exam  >  Class 9 Tests  >  Advance Learner Course: Mathematics (Maths) Class 9  >  Assertion & Reason Test: Polynomials - 2 - Class 9 MCQ

Assertion & Reason Test: Polynomials - 2 - Class 9 MCQ


Test Description

10 Questions MCQ Test Advance Learner Course: Mathematics (Maths) Class 9 - Assertion & Reason Test: Polynomials - 2

Assertion & Reason Test: Polynomials - 2 for Class 9 2024 is part of Advance Learner Course: Mathematics (Maths) Class 9 preparation. The Assertion & Reason Test: Polynomials - 2 questions and answers have been prepared according to the Class 9 exam syllabus.The Assertion & Reason Test: Polynomials - 2 MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Polynomials - 2 below.
Solutions of Assertion & Reason Test: Polynomials - 2 questions in English are available as part of our Advance Learner Course: Mathematics (Maths) Class 9 for Class 9 & Assertion & Reason Test: Polynomials - 2 solutions in Hindi for Advance Learner Course: Mathematics (Maths) Class 9 course. Download more important topics, notes, lectures and mock test series for Class 9 Exam by signing up for free. Attempt Assertion & Reason Test: Polynomials - 2 | 10 questions in 20 minutes | Mock test for Class 9 preparation | Free important questions MCQ to study Advance Learner Course: Mathematics (Maths) Class 9 for Class 9 Exam | Download free PDF with solutions
Assertion & Reason Test: Polynomials - 2 - Question 1
Save

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.

Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 1

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.

Assertion & Reason Test: Polynomials - 2 - Question 2
Save

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.

Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 2

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.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Assertion & Reason Test: Polynomials - 2 - Question 3
Save

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).

Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 3
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.

Assertion & Reason Test: Polynomials - 2 - Question 4
Save

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.
Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 4

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.

Assertion & Reason Test: Polynomials - 2 - Question 5
Save

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.
Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 5
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.

Assertion & Reason Test: Polynomials - 2 - Question 6
Save

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.
Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 6
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.

Assertion & Reason Test: Polynomials - 2 - Question 7
Save

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.
Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 7
Reason is false [a polynomial of nth 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.

Assertion & Reason Test: Polynomials - 2 - Question 8
Save

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
Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 8
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.

Assertion & Reason Test: Polynomials - 2 - Question 9
Save

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 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.
Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 9

product of zeros = 1/4

Quadratic polynomial be 4x2 + x + 1. So, both A and R are correct and R explains A.

Assertion & Reason Test: Polynomials - 2 - Question 10
Save

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.
Detailed Solution for Assertion & Reason Test: Polynomials - 2 - Question 10
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.

13 videos|79 docs|29 tests
Join Course
Information about Assertion & Reason Test: Polynomials - 2 Page
In this test you can find the Exam questions for Assertion & Reason Test: Polynomials - 2 solved & explained in the simplest way possible. Besides giving Questions and answers for Assertion & Reason Test: Polynomials - 2, EduRev gives you an ample number of Online tests for practice

Top Courses for Class 9

Download as PDF

Top Courses for Class 9

Important Questions for Assertion & Reason Test: Polynomials - 2

Find all the important questions for Assertion & Reason Test: Polynomials - 2 at EduRev.Get fully prepared for Assertion & Reason Test: Polynomials - 2 with EduRev's comprehensive question bank and test resources. Our platform offers a diverse range of question papers covering various topics within the Assertion & Reason Test: Polynomials - 2 syllabus. Whether you need to review specific subjects or assess your overall readiness, EduRev has you covered. The questions are designed to challenge you and help you gain confidence in tackling the actual exam. Maximize your chances of success by utilizing EduRev's extensive collection of Assertion & Reason Test: Polynomials - 2 resources.

Assertion & Reason Test: Polynomials - 2 MCQs with Answers

Prepare for the Assertion & Reason Test: Polynomials - 2 within the Class 9 exam with comprehensive MCQs and answers at EduRev. Our platform offers a wide range of practice papers, question papers, and mock tests to familiarize you with the exam pattern and syllabus. Access the best books, study materials, and notes curated by toppers to enhance your preparation. Stay updated with the exam date and receive expert preparation tips and paper analysis. Visit EduRev's official website today and access a wealth of videos and coaching resources to excel in your exam.

Online Tests for Assertion & Reason Test: Polynomials - 2 Advance Learner Course: Mathematics (Maths) Class 9

Practice with a wide array of question papers that follow the exam pattern and syllabus. Our platform offers a user-friendly interface, allowing you to track your progress and identify areas for improvement. Access detailed solutions and explanations for each test to enhance your understanding of concepts. With EduRev's Online Tests, you can build confidence, boost your performance, and ace Assertion & Reason Test: Polynomials - 2 with ease. Join thousands of successful students who have benefited from our trusted online resources.
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup