Question

If alpha and beta are the roots of x2-x+2 then alpha3 beta +alpha beta3

Answer 1

alpha and beta are the roots of
x² - x + 2

so,
alpha + beta = -(-1)/1 = 1
alpha.beta = 2/1 = 2

now ,
alpha³.beta + alpha.beta.³
=alpha.beta{alpha² +beta²}
=alpha.beta{ (alpha+beta)²-2alpha.beta}
=2{1 -2 × 2 } = -6