Question

If
$\alpha$
and
$\beta$
are the zeroes of quadratic polynomial
$ax^{2} + bx + c$

Then evaluate
$\alpha - \beta$

​

Answer 1

$good \: morning \: \\ \\ ( \alpha - \beta ) = \sqrt{( \alpha + \beta ) {}^{2} - 4 \alpha \beta } \\ \\ \alpha + \beta = - b \div a \\ \\ and \\ \\ \alpha \beta = c \div a \\ \\ ( \alpha - \beta ) = \ \sqrt{(b {}^{2} \div a {}^{2}) - 4c \div a } \\ \\ \alpha - \beta ) = \sqrt{b {}^{2} - 4ac } \div a$