Question

If alpha and beta are the zeros of x square -5x+4 find 1/alpha+1/beta+2alpha beta

Answer 1

$\alpha + \beta = 5 \: \: \: and \: \: \: \alpha \beta = 4 \\ \frac{1}{ \alpha } + \frac{1}{ \beta } + 2 \alpha \beta = \frac{ \alpha + \beta }{ \alpha \beta } + 2 \alpha \beta \\ = \frac{5}{4} + 2 \times 4 = \frac{37}{4}$