Question

8. If α and β are the zeros of the quadratic polynomial f(x) = ax2 +bx + c, then evaluate: i) α –β ii) 1�- 1�

Answer 1

Step-by-step explanation:

$\alpha + \beta = \frac{ - b}{c} \\ \alpha \beta = \frac{c}{a} \\ \\ \alpha - \beta = {( \alpha + \beta )}^{2} - 4 \alpha \beta \\ = ({ \frac{ - b}{a} })^{2} - 4 \frac{c}{a} \\ = \frac{ {b}^{2} }{ {a}^{2} } - \frac{4c}{a} \\ = \frac{ {b}^{2} - 16 { {c} }^{2} }{ {a}^{2} } \\ =$

$= \frac{(b - 4c)(b + 4c)}{ {a}^{2} }$

Answer 2

Step-by-step explanation:

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