Question

If α and β are the zeros of the polynomial f(x) = ax2+ bx + c,
Find the value of 1/α2+ 1/β2

Answer 1

$\alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a} \\ \frac{1}{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} } = \frac{ { \beta }^{2} + { \alpha }^{2} }{( { \alpha \beta ) }^{2} } \\ = \frac{ {( \alpha + \beta )}^{2} - 2 \alpha \beta }{ {( \alpha \beta )}^{2} }$