Problem:
The function satisfies for all real numbers . If the equation has exactly four distinct real roots, then the sum of these roots is
Answer Choices:
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Solution:
If is a root, then so is . That is, all the distinct roots come in pairs symmetric around (except for the self-symmetric value , if it is a root). Each pair has sum . Since there are exactly four distinct roots, is not a root, there are exactly two pairs, and the sum of all roots is .