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

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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.

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

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.

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

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).

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

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

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

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.

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.

What is an algebraic expression?

An algebraic expression consists of variables, constants and mathematical operators.

What is a polynomial?

Polynomial is an algebraic expression in which the exponent on any variable is a whole number.

How to find the degree of polynomial from an algebraic expression?

Highest power of x in the given algebraic expression.

How many types of polynomials are there on the basis of number of terms?

There are three types- monomial, binomial and trinomial.

How many types of polynomials are there on the basis of degree of polynomial?

There are three types- Linear, Quadratic and Cubic polynomials.

What is zero of a polynomial?

A zero of a polynomial p(x) is the value of x for which the value of the polynomial p(x) is 0.

How many zeros can a linear polynomial have?

One zero

How many zeros can a quadratic polynomial have?

At most two zeros.