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)=x2−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

Correct option is A)

We have,

f(x)=x2−p(x+1)−c=0

f(x)=x2−px−(p+c)=0             .............(1)

Since,

α,β are the zeroes of the above polynomial.

So,

α+β=p 

αβ=−(p+c) 

Since,

(α+1)(β+1)=0

αβ+α+β+1=0

−p−c+p+1=0

−c+1=0

c=1

Hence, this is the answer.