Question

alpha and beta are zeros of polynomial p x = 2 x square - 7 x + 3 find the value of alpha cube + beta cube

Answer 1

alpha= 3 beta= 1/2
alpha cube+beta cube=3³+(1/2)³
=27+1/8
=217/8
Hope it helps u and make it as brainliest!

Answer 2

Solution:-

given by equation:-

$p(x) = 2 {x}^{2} - 7x + 3 \\ root \: are \: \alpha ans \: \beta \\ then \\ \alpha + \beta = \frac{ - b}{a} = \frac{ 7}{2} \\ \alpha . \beta = \frac{c}{a} = \frac{3}{2} \\ we \: have \\ { \alpha }^{3} + { \beta }^{3} = {( \alpha + \beta )}^{3} - 3 \alpha \beta ( \alpha + \beta ) \\ = { (\frac{7}{2} )}^{3} - 3 \times \frac{3}{2} \times \frac{7}{2} \\ { \alpha }^{3} + { \beta }^{3} = \frac{343}{8} - \frac{63}{4} \\ { \alpha }^{3} + { \beta }^{3} = \frac{343 - 126}{8} \\ { \alpha }^{3} + { \beta }^{3} = \frac{217}{8} \\ ( { \alpha }^{3} + { \beta }^{3} = 27 \frac{1}{8} )ans$