Question

if alpha and beta are the zeros of the polynomial f(X)=x2-3x+6find the value of 1/alpha+1/beta+alpha2+beta2-2alpha beta

(Pls answer)

Answer 1

$f(x) = {x}^{2} - 3x + 6 \\ \alpha + \beta = 3 \: \: \: \: \: \: \: \: \alpha \beta = 6 \\ \frac{1}{ \alpha } + \frac{1}{ \beta } + { \alpha }^{2} + { \beta }^{2} - 2 \alpha \beta \\ = \frac{ \alpha + \beta }{ \alpha \beta } + {( \alpha + \beta )}^{2} - 4 \alpha \beta \\ = \frac{3}{6} + {3}^{2} - 4 \times 6 = \frac{ - 29}{2}$