Question

The number of polynomials having zeroes as -2 and 5 is:
(A)1
(B)2
(C)3
(D) more than 3
Please give proper reasons.

Answer 1

Answer:

Option(D)

Step-by-step explanation:

Zeroes are -2 and 5.

Let us take α,β as roots.

Sum of zeroes:

α + β = -b/a

-2 + 5 = -b/a

3 = -b/a

Product or roots :

αβ = c/a

=> -2 * 5 = c/a

=> c/a = -10

Thus, the required equation is,

=> x² - (b/a)x + (c/a) = 0

=> x² + 3x - 10 = 0

We know, the zeroes do not change if the polynomial is divided or multiplied by a constant.

p(x) = kx² - 3kx - 10k {k is a real number}

p(x) = x²/k - (3/k)x - (10/k)

Thus, the number of polynomials are more than 3.

Hope it helps!