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prod (x-a_1)=prod (x+a_1) - All-Russian MO 2000 Regional (R4) 11.1

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September 26, 2024
algebrapolynomial

Problem Statement

Prove that it is possible to choose different real numbers a1,a2,...,a10a_1, a_2, . . . , a_{10} that the equation (x−a1)(x−a2)....(x−a10)=(x+a1)(x+a2)...(x+a10)(x - a_1)(x -a_2).... (x -a_{10}) = (x + a_1)(x + a_2) ...(x + a_{10}) will have exactly 55 different real roots.
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