Question

if alpha and beta are zeroes of polynomial fx =x2 - p(x+2)-c then find the value of (alpha +2)(beta+2).

Answer 1

${x}^{2} - p(x + 2) - c \\ {x}^{2} - px - (2p + c) \\ \alpha + \beta = p \\ \alpha \beta = - (2p + c) \\ ( \alpha + 2)( \beta + 2) \\ = \alpha \beta + 2( \alpha + \beta ) + 4 \\ = - (2p + c) + 2p + 4 \\ = 4 - c$
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