Question

if alpha and beta are the zeroes of the polynomial x^2 - p(x+1) - c . such that (alpha-1) (beta+1) = 0 . find the value of c

Answer 1

${x}^{2} - p(x + 1) - c = 0 \\ {x}^{2} - px - (p + c) = 0 \\ \alpha + \beta = p \\ \alpha \beta = - (p + c )$
Now given that
$( \alpha - 1)( \beta + 1) = 0 \\ \alpha = 1 \\ \beta = - 1$
Now put the value of alpha and beta in the previous equation.
$\alpha + \beta = p \\ 1 - 1 = p \\ p = 0$
Now substitute this in the second equation to get the value of c.
$\alpha \beta = - (p + c) \\ - 1 = - c \\ c = 1$
If this helps, please mark it as the brainliest answer. I would really appreciate it.