Chapter 2 Polynomials Assertation & Reasoning Questions Class 10th

Direction: 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.

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

Answer: (d)

2.) Assertion: If the sum of the zeroes of the quadratic polynomial x^2-2kx+8 is 2 then value of k is 1.

Reason: Sum of zeroes of a quadratic polynomial ax^2+bx+c is-b/a

Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.

3.)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: (a)

4.)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: (d)

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

Answer: (c)

6.)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: (b)

7)Assertion: Degree of aa zero polynomial is not defined.

Reason: Degree of a non-zero constant polynomial is 0.

Ans: b) both Assertion and reason are correct but  reason is not correct explanation for assertion.

8) 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

Ans: c) Assertion is correct but reason is false

9) 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.           

Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.

10) 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: (b)

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

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

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

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

14) Assertion:x+1is a Linear Polynomial

Reason (R): The polynomials of degree 1 are called linear polynomials.

Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion

15) Assertion: The graph of a polynomial p(x) is a straight line parallel to x axis. The polynomial has no zeros.

Reason (R): If a polynomial P(x) does not intersect the x-axis at any point, it does not have any zero.

Ans: a ) both  Assertion and reason are correct and  reason is correct explanation for assertion