Question

If α and β are the roots of a quadratic polynomial ax^2+bx+c, then find the value of α^2 + β^2.

Answer 1

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