An algebra problem by Patrick Prochazka

Algebra Level pending

Find the sum of the roots of x 80 − 2 x 79 + 3 x 78 − . . . + 79 x − 80 x^{80} - 2x^{79} + 3x^{78} - ... +79x-80 .


The answer is 2.

Patrick Prochazka by Patrick Prochazka , 20, Canada

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1 solution

Patrick Prochazka
Jul 15, 2015

By Vieta's formulas, the sum of the roots is − − 2 1 - \frac{-2}{1} , or 2 2 .

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Moderator note:

Bonus question : Prove that the polynomial only have one real root.

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