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If the roots of $x^{2} - p (x + 1) + c = 0$ are $α and β$ then the value of $α^{2} + (2 + p) α β + β^{2}$ is

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$p c$

$p^{2} + p c$

$p^{2} - p c$

$- p c$

answer is A.

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Detailed Solution

$\begin{array}{l} α + β = p \\ α β = c - p \\ α^{2} + 2 α β + β^{2} + p α β \\ = {(α + β)}^{2} + p (c - p) \\ = p^{2} + p c - p^{2} \\ = p c \end{array}$

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