If α, β are the zeros of the polynomial f(x) = x² – p (x + 1) – c such that (α + 1) (β + 1) = 0, then c =

Question

If α, β are the zeros of the polynomial f(x) = x 2 – p (x + 1) – c such that (α + 1) (β + 1) = 0, then c =

Philoid · Accepted Answer

Given

f(x) = x² – p (x + 1) – c

α and β are the zeros

Then,

f(x) = x² – p (x + 1) – c

= x² – px – (p + c)

As

(α + 1)(β + 1) = αβ + α + β + 1

= – p – c + p + 1

= 1 – c

So, the value of c,

c = 1

If α, β are the zeros of the polynomial f(x) = x2 – p (x + 1) – c such that (α + 1) (β + 1) = 0, then c =