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PD0022 · Problem 105

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Problem

The quadratic equation (5a+10b)x2+(7a14b)x6ab=0(5a+10b)x^2 + (7a-14b)x - 6ab = 0 has two real solutions whose sum is 14b7a15a+30b.\dfrac{14b-7a}{15a+30b}. Which of the following must be true?
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