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Assertion & Reason Test: Polynomials - Class 10 MCQ


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10 Questions MCQ Test Mathematics (Maths) Class 10 - Assertion & Reason Test: Polynomials

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

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


Assertion & Reason Test: Polynomials - Question 2
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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.

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

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

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

Assertion & Reason Test: Polynomials - Question 4
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Assertion (A): A polynomial of degree n cannot have more than n terms.

Reason (R): The number of coefficients in a polynomial is always one more than its degree.
Detailed Solution for Assertion & Reason Test: Polynomials - Question 4

Assertion & Reason Test: Polynomials - Question 5
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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).
Detailed Solution for Assertion & Reason Test: Polynomials - Question 5
Let α, 1/α be the zeroes of p(x) then we have

Product of Zeroes

⇒ k2 – 4k + 4 = 0

⇒ (k – 2)2 = 0 ⇒ k = 2

Assertion & Reason Test: Polynomials - Question 6
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Assertion (A): The polynomial x2−5x + 6 can be factored as (x−2) (x−3)

Reason (R): The roots of the polynomial are 2 and 3, which can be used to express the polynomial in its factored form.
Detailed Solution for Assertion & Reason Test: Polynomials - Question 6

Assertion & Reason Test: Polynomials - Question 7
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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
Detailed Solution for Assertion & Reason Test: Polynomials - Question 7

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.

Assertion & Reason Test: Polynomials - Question 8
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Assertion (A): A polynomial of degree 3 can have at most two real roots.

Reason (R): According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n roots, which can be real or complex.
Detailed Solution for Assertion & Reason Test: Polynomials - Question 8

Answer: d) Assertion is incorrect, but Reason is correct.

Explanation:
A polynomial of degree 3 can have at most three real roots. The assertion stating that it can have at most two real roots is incorrect.

Assertion & Reason Test: Polynomials - Question 9
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Assertion (A): The zeroes of the polynomial  p(x) = (x - 1)(x - 2)(x - 3)  are 1, 2, and 3.
Reason (R): The zeroes of a polynomial are the x-coordinates of the points where the graph of the polynomial intersects or touches the x-axis or the points on the graph where  p(x) = 0 
Detailed Solution for Assertion & Reason Test: Polynomials - Question 9

Option A: Both A and R are true and R is the correct explanation for A.

The polynomial p(x) = (x - 1)(x - 2)(x - 3) \) is factored into three linear factors: (x - 1) , (x - 2) , and  (x - 3) .

The zeroes of a polynomial are the values of  x  for which p(x) = 0. Setting each factor equal to zero gives the zeroes as x = 1 , x = 2 , and x = 3 , which confirms Assertion (A) as correct.

The reason (R) correctly explains the concept that the zeroes of a polynomial are the x-coordinates where the polynomial graph intersects or touches the x-axis, or where p(x) = 0.

Therefore, both the assertion and reason are correct, and the reason provides the correct explanation for the assertion.

Assertion & Reason Test: Polynomials - Question 10
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Assertion (A): The degree of a polynomial is always 0

Reason (R): A polynomial does not have any exponents. 
Detailed Solution for Assertion & Reason Test: Polynomials - Question 10

- Assertion (A) is incorrect: The degree of a polynomial is not always 0. The degree of a polynomial is the highest power of the variable with a non-zero coefficient. 

- Reason (R) is incorrect: A polynomial can have exponents. These exponents are what define the degree of the polynomial.
- Correct Answer: Neither Assertion nor Reason is correct.

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