Assertion and Reason Questions for Class 10 Maths Chapter 2 Polynomials

Board	CBSE
Useful for	Class 10 Students
Subject	Maths
Chapter	Chapter 2 Polynomials
Type of Questions	Assertion and Reason
Format	Question-Answer Format
Important Link	Class 10 Maths Chapterwise Assertion Reason

Assertion and Reason Questions for Class 10 Maths Chapter 2 Polynomials

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(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.

Q.1. Assertion: x²+7x+12 has no real zeroes.
Reason: A quadratic polynomial can have at the most two zeroes.

Answer

Answer: (d)

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Q.2. 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

Answer

Answer: (a)

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Q.3. 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.

Answer

Answer: (d)

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Q.4. Assertion: x³+x has only one real zero.
Reason: A polynomial of nth degree must have n real zeroes.

Answer

Answer: (c)

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Q.5. 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).

Answer

Answer: (b)

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Q.6. Assertion: x²+4x+5 has two zeroes.
Reason: A quadratic polynomial can have at the most two zeroes.

Answer

Answer: (d)

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Q.7. Assertion: Degree of aa zero polynomial is not defined.
Reason: Degree of a non-zero constant polynomial is 0.

Answer

Answer: (b)

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Q.8. 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

Answer

Answer: (b)

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Q.9. Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes 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.

Answer

Answer: (c)

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Q.10. Assertion: 3-2√5 is one zero of the quadratic polynomial then other zero will be 3+2√5.
Reason: Irrational zeros (roots) always occurs in pairs.

Answer

Answer: (a)

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Q.11. Assertion: (2 − √3) is one zero of the quadratic polynomial then other zero will be (2 + √3) .
Reason: Irrational zeroes (roots) always occurs in pairs.

Answer

Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

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Q.12. Assertion: If one zero of polynomial p(x) = (k + 4) x² + 13x + 3k 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).

Answer

Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Q.13. Assertion: A polynomial of degree 5 is divided by a quadratic polynomial. If it leaves a remainder, then the degree of remainder is 1 or 0.
Reason: Degree of remainder is always less than divisor.

Answer

Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Q.14. Assertion: The polynomial p(x) = 5x – 1/2 is a linear polynomial.
Reason: The general form of linear polynomial is ax+b.

Answer

Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Q.15. Assertion: The graph of a polynomial intersect x-axis at 3 points and y-axis at 1 points, the polynomial has 3 zeroes.
Reason: The number of zeroes that a polynomial p(x) can have is the number of times polynomial intersect x and y axis.

Answer

Answer: (c) Assertion is correct but reason is wrong.

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