Question

if alpha beta are zeroes of the quadratic polynomial f(x) = 2x2+11x+5 a) alpha4+ beta 4

Answer 1

Answer:

$\alpha \: and \: \beta \: are \: the \: zeroes \: of \: the \: eqution \\ \: 2 {x}^{2} + 11x + 5 = 0$

$2 {x}^{2} + 11x + 5 = 0$

$camparing \: with \: a{x}^{2} + bx + c = 0$

$a = 2 \\ b = 11 \\ c = 5$

$\alpha + \beta = \frac{ - b}{a}$

$\alpha + \beta = \frac{ - 11}{2}$

$multiplying \: throughtout \: by \: 4$

$4(\alpha + \beta ) = 4 \times \frac{ - 11}{2}$

[tex]4 \alpha + 4 \beta = {-22}