Let the roots of quadratic equation $x^2 + px + q$ be equal to $r$ and $s$.
Using Vieta's formulas, what is the value of $r - s$ in terms of $p$ and $q$?
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Hint: Can you find $(r-s)^2$ using Vieta formulas? – Sep 16 '20 at 12:55
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oh damn thanks lol – John Liu Sep 16 '20 at 12:56
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Alternatively, since the zeroes are given by $$ r , s \ \ = \ \ -\frac{p}{2} \ \pm \ \frac{\sqrt{p^2 \ - \ 4q }}{2} \ \ = \ \ -\frac{p}{2} \ \pm \ \frac{\sqrt{\Delta }}{2} \ \ , $$ we have $ \ r - s \ = \ \sqrt{\Delta} \ \ , $ a frequently useful "quadratics fact". – Sep 27 '21 at 04:48