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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.
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Assertion & Reason Test: Polynomials - Question 1

Directions: 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 - Question 1

The assertion is false because the quadratic equation x+ 7x + 12 can be factored as (x + 3)(x + 4), which means it has two real zeros (-3 and -4). The reason is true because a quadratic polynomial indeed can have at most two zeros, but it doesn't directly relate to the assertion being true or false.

Assertion & Reason Test: Polynomials - Question 2

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 2


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Assertion & Reason Test: Polynomials - Question 3

Directions: 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) = 4x3-x2+5x4+3x-2 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 - Question 3

The assertion is false because the degree of the polynomial is determined by the highest power of x, which is 4 in this case, making it a polynomial of degree 4. The reason is true because the highest power of x indeed determines the degree of a polynomial, but it incorrectly describes the polynomial in the assertion.

Assertion & Reason Test: Polynomials - Question 4

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 4
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.
Assertion & Reason Test: Polynomials - Question 5

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 one zero of polynomial p(x) = (k2+4)x2+13x+4k is reciprocal of the 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

The assertion and reason are both true, but the reason does not directly explain k=2 when one zero is the reciprocal of the other. The calculation to find k would involve using the relationship between the product of the roots and the constants in the polynomial, which is not mentioned in the reason.

Assertion & Reason Test: Polynomials - Question 6

Directions: 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 - Question 6

The assertion is false because x2 +4x+5 has no real zeroes (its discriminant, b 2 −4ac, is negative). However, it has two complex zeroes. The reason is true, as a quadratic polynomial can have at most two zeroes (real or complex).

Assertion & Reason Test: Polynomials - Question 7

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 7

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 8

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 8
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 9

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 9

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 10

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 zeroes.

Reason : A quadratic polynomial can have at the most two zeroes.

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

Assertion: Consider the given polynomial x2 + 4x + 5

Because the degree of the polynomial is 2. It is a quadratic polynomial. We know that the quadratic polynomial has at the most two zeroes.

∴ x2 + 4x + 5 has two zeroes.

∴ Assertion is false as its Discriminant is -ve.

Reason: Clearly, Reason is true.

Since Assertion (A) is false but reason (R) is true.

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