Question

if alpha and beta are the roots of the equation 4x square - 5 x + 2 is equal to zero find the equation whose roots are alpha + 3 Beta and 3 alpha +beta​

Answer 1

$\alpha \: and \: \beta \: are \: root \: of \: quadratic \: equation \: 4 {x}^{2} - 5x + 2 = 0 \\ now \\ comparing \: with \: a {x}^{2} + bx + c = 0 \\ a \: = 4 \: \: b = - 5 \: \: c = 2 \\ now \\ \alpha + \beta = \frac{ - b}{a} \\ = \frac{ - ( - 5)}{4} \\ = \frac{5}{4} \\ now \: \\ \alpha . \beta = \frac{c}{a} \ \\ = \frac{2}{4} \\ = \frac{1}{2}$