Question

If alpha and beta are the roots of x^2+5x+a=0 and 2alpha+5beta=-1,then find the value of 'a' .

Answer 1

$fro m\: \: the \: \: equation \\ \alpha + \beta = - 5 - - - (1) \\ given \: \: 2 \alpha + 5 \beta = - 1 - - - (2) \\ (2) - 2 \times (1) \: \: gives \\ 3 \beta = 9 \\ \beta = 3 \\ from \: \: (1) \: \: \\ \alpha = - 5 - \beta = - 5 - 3 = - 8 \\ \\ from \: \: the \: \: equation \\ \alpha \beta = a \\ thus \: \: \: a = - 8 \times 3 = - 24$