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Reciprocated quadratic roots (Posted on 2024-11-24)

Let P(x) be a quadratic with real, nonzero roots and coefficients such that P(-20)+P(21)=P(-29). Find sum of the reciprocals of the roots of P(x).

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 2

Let P(x)=a(x-p)(x-q)

The equation becomes

a(-20-p)(-20-q)+a(21-p)(21-q)=a(-29-p)(-29-q)

pq=30p + 30q

(p+q)/pq = 1/p + 1/q = 1/30

Posted by Jer on 2024-11-24 11:37:35

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