Find the sum of all real numbers x such that 5x4−10x3+10x2−5x−11=0.
A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution
Rearrange the equation to x5+(1−x)5−12=0. It's easy to see this has two real roots, and that r is a root if and only if 1−r is a root, so the answer must be 1.
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