Question

$if \: \alpha \beta \: are \: the roots \: of \: \: ax {}^{2} + b \times + c = 0 \: then \: | \alpha - \beta | =$
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Answer 1

Step-by-step explanation:

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

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