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 =

Given

f(x) = x^{2} – p (x + 1) – c

α and β are the zeros

Then,

f(x) = x^{2} – p (x + 1) – c

= x^{2} – 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

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