If α,β are the zeros of the polynomial f(x)=x 2 −p(x+1)−c=0 such (α+1)(β+1)=0, then c= A 1 B 0 C −1 D 2

Question

If $α, β$ are the zeros of the polynomial $f (x) = x^{2} - p (x + 1) - c = 0$ such $(α + 1) (β + 1) = 0$ , then $c =$

A

$1$

B

$0$

C

$- 1$

D

$2$

Medium

Solution

Verified by GMS

Since,
$α, β$ are the zeroes of the above polynomial.

So,
$α + β$
$α β = - (p + c)$

Since,
$(α + 1) (β + 1) = 0$

$α β + α + β + 1 = 0$

$- p - c + p + 1 = 0$

$- c + 1 = 0$

$c = 1$

Hence, this is the answer.

Getting Info...

Copy