Question

if alpha and beta are the zeroes of the polynomial x^2 - p (x+1)- c, then find the value of (alpha +1)(beta + 1)

Answer 1

${x}^{2} - px - (p + c) = 0 \\ \alpha \beta = - (p + c) \\ \alpha + \beta = p$
Now
$( \alpha + 1)( \beta + 1) = \alpha \beta + ( \alpha + \beta ) + 1 \\ = - p - c + p + 1 \\ = 1 - c$