Question

If alpha and beta are zeroes of x2-6x+a find the value of a if 3α +2β=20

Answer 1

refer to the attachment

Answer 2

two roots

$\alpha \: \beta$

$\alpha + \beta = {6 \div 1} = 6$

$\alpha \beta = a$

$3 \alpha + 2 \beta = 20 \\ 2 \alpha + 2 \beta + \beta = 20 \\ 2( \alpha + \beta ) + \beta = 20 \\ 2 \times 6 + \beta = 20 \\ \beta = 8 \\ \alpha \beta = a \\ \alpha = - 2 \\ \\a = - 16$