Question

If alpha and beta are the zeroes of x^2 +7x + 12, then find the value of 1/alpha +1/beta +2 alpha beta

Answer 1

$\alpha + \beta = - 7 \\ \alpha \beta = 12$
$= \frac{1}{ \alpha } + \frac{1}{ \beta } + 2 \alpha \beta \\ = \frac{ \alpha + \beta }{ \alpha \beta } + 2 \alpha \beta \\ = \frac{ - 7}{12} + 2(12) \\ = \frac{ - 7}{12} + 24 \\ = \frac{ - 7 +288 }{12} \\ = \frac{281}{12}$