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Given \[r = \frac{-b + \sqrt{b^2 - 4ac}}{2a} \text{ and } s = \frac{-b - \sqrt{b^2 - 4ac}}{2a}.\] What is the value of $r+s$, simplified in terms of $a, b$, and $c$?

 Feb 24, 2021
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r and s are both the roots of the polynomial \(ax^2+bx+c\), so r+s is just the sum of the 2 roots. According to Vieta's formulas, that is equal to \(\boxed{\frac{-b}{a}}\)

 Feb 24, 2021

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