If α, β are the zeros of polynomial f(x) = x2 − p (x + 1) − c, then (α + 1) (β + 1) =

Solution:

Since $\alpha$ and $\beta$ are the zeros of quadratic polynomial

$f(x)=x^{2}-p(x+1)-c$

$=x^{2}-p x-p-c$

$\alpha+\beta=\frac{-\text { Coefficient of } x}{\text { Coefficient of } x^{2}}$

$=-\left(\frac{-p}{1}\right)$

$=p$

$\alpha \times \beta=\frac{\text { Constant term }}{\text { Coefficient of } x^{2}}$

$=\frac{-p-c}{1}$

$=-p-c$

We have

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

$=\alpha \beta+\beta+\alpha+1$

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

$=-p-c+(p)+1$

$=-c+1$

$=1-c$

The value of $(\alpha+1)(\beta+1)$ is $1-c$

Hence, the correct choice is $(b)$