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


If $\alpha, \beta$ are the zeros of polynomial $f(x)=x^{2}-p(x+1)-c$, then $(\alpha+1)(\beta+1)=$

(a) $c-1$

(b) $1-c$

(c) $C$

(d) $1+c$


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


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

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



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



We have


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

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




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

Hence, the correct choice is $(b)$


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