Question

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$if \: \alpha \: and \: \beta \: are \: the \: roots \: of \: a {x }^{2} - bx + c = 0 \: then \: calculate \: \alpha + \beta$
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Answer 1

Hey mate this is your answer hope it helps.

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Answer 2

$\mathcal {\purple {SOLUTION:-}} \\ \\ \\ </p><p> \tt \alpha \: and \: \beta \: are \: the \:roots \\ </p><p> \tt \:of \: the \: Equation \: \implies\: ax^2 + bx + c = 0 \\ \\</p><p> </p><p> \tt \therefore \: \: \alpha \:= \:\frac{-b + \sqrt{b^2 - 4ac}}{2a} \\ \\</p><p> \tt \therefore \: \: \beta \: = \: \frac{-b - \sqrt{b^2 - 4ac}}{2a} \\ \\</p><p></p><p> \tt \red{{now,}} \\ \\ </p><p></p><p> \tt \: \alpha + \beta\: = \: \frac{-b + \sqrt{b^2 - 4ac}}{2a} + \frac{-b - \sqrt{b^2 - 4ac}}{2a} \\ \\</p><p></p><p>\tt \: = \: \frac{-b + \sqrt{b^2 - 4ac} - b - \sqrt{b^2 - 4ac}}{2a} \\ \\ </p><p></p><p>\tt \: = \: - \frac{2b}{2a} \\ \\ </p><p></p><p>\tt \therefore \pink {\boxed {\alpha + \beta \: = \: - \frac{b}{a}}}$