Page 17 - Mathematics Class - X

Viva-Voce

1. Define zero of a polynomial.
Ans. A real number k is called a zero of a polynomial p(x), if p(k) = 0.
2. What is the degree of a quadratic polynomial?

Ans. The degree of a quadratic polynomial is 2.
3. How many zeroes can a polynomial of degree 2 have at the most?
Ans. A polynomial of degree 2 can have at the most 2 zeroes.

4. If 1 is a zero of the polynomial x – 1, what is the point at which the curve of the polynomial intersects
2
X-axis?
Ans. Let y = x – 1.
2
When x = 1, then y = 1 – 1 = 0. Thus, the required point is (1, 0).
2
1
5. If the sum and product of the zeroes of a quadratic polynomial are and – 1 respectively, form the
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polynomial.

Ans. We know that a quadratic polynomial with the sum and product of its zeroes is given by
f (x) = k{x – (sum of the zeroes) x + Product of the zeroes}, where k is a constant.
2
1
i.e., f ( )x = { kx − 2 x − 1}
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MCQs

1. The number of polynomials having zeroes as –2 and 5 is
a) 1 b) 2 c) 3 d) more than 3

2. If the zeroes of the quadratic polynomial x + (a + 1) x + b are 2 and –3, then
2
a) a = –7, b = –1 b) a = 5, b = –1 c) a = 2, b = – 6 d) a = 0, b = – 6
3. The zeroes of the quadratic polynomial x + 99x + 127 are
2
a) both positive b) both negative
c) one positive and one negative d) both equal
4. The zeroes of the quadratic polynomial x + kx + k, k ≠ 0,
2
a) cannot both be positive b) cannot both be negative
c) are always unequal d) are always equal
5. If the zeroes of the quadratic polynomial ax + bx + c, c ≠ 0 are equal, then
2
a) c and a have opposite signs b) c and b have opposite signs

c) c and a have the same sign d) c and b have the same sign

Answers: 1. d) more than 3 2. d) a = 0, b = – 6 3. b) both negative
4. a) cannot both be positive 5. c) c and a have the same sign

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