Question

If the polynomial f(x)=x^2+kx-15,  is exactly divisible by x-5, then the value of k is _______

(a) 3

(b) 2

(c) -3

(d) -2

This question was posed to me in an international level competition.

I'm obligated to ask this question of Division of Polynomial topic in chapter Polynomials of Mathematics – Class 10

Answer 1

Correct choice is (d) -2

The explanation: x^2+kx-15 is exactly divisible by x-5

Dividing, x^2+kx+15 by x-5

We get, 5k+10 as remainder.

Since,  x^2+kx-15 is exactly divisible by 2x-5

∴ 5k+10=0

k=-2