Question

If alpha and beta be the zeros of polynomial 2x square + 5x + k such that alpha square + beta square + alpha multiplied by beta = 21/4, then k? Please answer quick... urgent!

Answer 1

$\alpha + \beta = \frac{-5}{2} \\ \alpha \beta = \frac{k}{2}$
$\alpha ^{2} + \beta^{2} + \alpha\beta = ( \alpha + \beta)^{2} - \alpha\beta \\ = ( \frac{-5}{2} )^{2} - \frac{k}{2} = 21/4 \\ k = 2$