Question

If α and β are the zeros of the quadratic polynomial f(x) = ax^2 + bx + c, then evaluate: (i) α-β

Answer 1

$\alpha + \beta = \frac{ - b}{a} \: \: \: \: \: \: \: \alpha \beta = \frac{c}{a} \\ {( \alpha - \beta )}^{2} = {( \alpha + \beta )}^{2} - 4 \alpha \beta \\ = {( \frac{ - b}{a} )}^{2} - 4 \times \frac{c}{a} = \frac{ {b}^{2} - 4ac }{ {a}^{2} } \\ thus \: \: \alpha - \beta = \frac{ \sqrt{ {b}^{2} - 4ac }}{a}$