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

Question

If α,β are zeros of the polynomial f(x)=x2−c(x+1)−c, then (α+1)(β+1)=

A

1+c

B

1−c

C

c−1

D

c

Medium

Solution

Verified by  GMS

Correct option is B)

If α, β are the zeros of the quadratic polynomial f(x)=x2−c(x+1)−c=x2−cx−c−c=x2−cx−2c, then,
(α+β)=a−b​=−1−c​=c,αβ=ac​=1−2c​=−2c
Now,
    (α+1)(β+1)
=αβ+α+β+1
=−2c+c+1
=1−c