Assertion and Reason Questions for Class 10 Maths Chapter 2 Polynomials PDF

Assertion and Reason Questions for Class 10 Maths Chapter 2 Polynomials are available in this Maths article. Assertion and Reason Questions for Class 10 Maths Chapter 2 Polynomials are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Polynomials. Polynomials cover expressions with variables and powers, along with ideas like zeroes, degree, and factorisation, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. A free downloadable PDF is also available for easy practice and revision. 

Important Assertion And Reason Questions on Polynomials

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

Choose the correct option for the following questions:

• (A). Both Assertion (A) and Reason (R) are true, and Reason is the correct explanation of Assertion.

• (B). Both Assertion (A) and Reason (R) are true, but Reason is not the correct explanation of Assertion.

• (C). Assertion (A) is true, but Reason (R) is false.

• (D). Assertion (A) is false, but Reason (R) is true.

Question 1:

Assertion (A): A polynomial of degree 2 is called a quadratic polynomial.

Reason (R): The highest power of the variable in a quadratic polynomial is 2.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 2:

Assertion (A): The polynomial x2−5x+6has zeros 2 and 3.

Reason (R): If p(x)=0, then the value of (x) is called a zero of the polynomial.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (B). Both A and R are true, but R is not the correct explanation of A. x2−5x+6=(x−2)(x−3)

Question 3:

Assertion (A): The graph of a linear polynomial is a straight line.

Reason (R): A linear polynomial has degree 1.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 4:

Assertion (A): A cubic polynomial can have at most three zeros.

Reason (R): The degree of a polynomial is equal to the maximum number of zeros it can have.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 5:

Assertion (A): If one zero of the polynomialx2−9is 3, then another zero is−3.

Reason (R): x2−9can be factorised as:

x2−9=(x−3)(x+3)

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 6:

Assertion (A): The sum of the zeros ofx2−7x+10is 7.

Reason (R): For a quadratic polynomialax2+bx+c, the sum of zeros is:−ba

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 7:

Assertion (A): The product of the zeros of x2−7x+10is 10.

Reason (R): For a quadratic polynomialax2+bx+c, the product of zeros is:ca

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 8:

Assertion (A): Every polynomial has at least one zero.

Reason (R): The graph of every polynomial intersects the x-axis.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (D). A is false, but R is true.

Question 9:

Assertion (A): If x−2 is a factor of a polynomial  p(x), thenp(2)=0).

Reason (R): According to the Factor Theorem, ifp(a)=0, then(x−a)is a factor of p(x).

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 10:

Assertion (A): A constant polynomial has degree 0.

Reason (R): The variable in a constant polynomial has power 0.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 11:

Assertion (A): The polynomialx2+2x+1has equal zeros.

Reason (R):x2+2x+1can be written as:(x+1)2

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 12:

Assertion (A): A polynomial of degree 3 is called a cubic polynomial.

Reason (R): The highest exponent of the variable determines the degree of the polynomial.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 13:

Assertion (A): The zero of the polynomialx−5is 5.

Reason (R): A zero of a polynomial is the value of the variable that makes the polynomial equal to zero.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 14:

Assertion (A): The polynomialx2+4x+4has only one distinct zero.

Reason (R): x2+4x+4can be factorised as: (x+2)2

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A.

Question 15:

Assertion (A): Ifx+1is a factor of the polynomialx2+x−2, thenp(−1)=0.

Reason (R): According to the Factor Theorem, if  (x−a) is a factor ofp(x), thenp(a)=0.

Options:

(A). Both A and R are true, and R is the correct explanation of A.
(B). Both A and R are true, but R is not the correct explanation of A.
(C). A is true, but R is false.
(D). A is false, but R is true.

Correct Answer: (A). Both A and R are true, and R is the correct explanation of A. x2+x−2=(x+2)(x−1)

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