Q7 of 109 Page 3

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 =

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

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