5.59 Two people play a game according to the following rules: Player A first gives 3 different non-zero digits, and Player B then fills them into the positions marked with asterisks in the following quadratic trinomial:
(which number goes in which position is chosen by Player B).
If the resulting quadratic trinomial has two distinct rational roots, then Player A wins. Prove that Player A can ensure his victory.
Solution
[Proof] If Party A says the numbers 1, 2, and -3, they will win. Generally, Party A can say any 3 different non-zero rational numbers whose sum is 0. At this point, the equation must have a root . By Vieta's formulas, the other root is .
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