Question

If α, β are the zeroes of polynomial f(x) = x2–px–c, then find the value of (α + 1) (β + 1).

Answer 1

f(x)= x²- px-c

We know that

sum of roots = -b/a

$\alpha + \beta = \frac{ - b}{a} \\ \\ \alpha + \beta = - p$

product of roots = c/a

$\alpha \beta = \frac{c}{a} \\ \alpha \beta = - c$

(

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