Question

If α and β are zeroes of the polynomial p(x) = ax2 – bx + c, then calculate α +
β

Answer 1

Answer:

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