Question

If alpha and beta are the zeroes of the polynomial p(x) = x square - px - (p + c) then find the value of (alpha + 1) (beta + 1)

Answer 1

Answer.

p(x) = x² – px – (p + c)

Since α and β are the zeroes of p(x).

Therefore,

$\alpha + \beta = \frac{ - ( - p)}{1} = p$

And,

$\alpha \beta = \frac{ - (p + c)}{1} = - p - c$

Now,

$( \alpha + 1)( \beta + 1) = \alpha \beta + \alpha + \beta + 1$

$= - p - c + p = - c$

∴ (α + 1)(β + 1) = –c

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