Question

If alpha and beta are the zeros of x^2 +px+q then find the value of (alpha/beta+2) (beta/alpha+2)

Answer 1

$\alpha + \beta = - p \\ \alpha \beta = q \\ (\frac{ \alpha }{ \beta + 2}) ( \frac{ \beta }{ \alpha + 2} ) = \frac{ \alpha \beta }{( \alpha \beta + 2 \alpha + 2 \beta + 4} \\ = \frac{q}{q + 2( \alpha + \beta) + 4 } \\ = \frac{q}{q + 2( - p) + 4} \\ (\frac{ \alpha }{ \beta + 2}) ( \frac{ \beta }{ \alpha + 2} ) = \frac{q}{q - 2p + 4}$