Let be the roots of

MATHEMATICS · Single correct · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

Let α,β\alpha,\beta be the roots of x2−px+r=0x^2-px+r=0, and let α2,2β\frac{\alpha}{2},2\beta be the roots of x2−qx+r=0x^2-qx+r=0. The value of rr is: (1) 29(p−q)(2q−p)\frac{2}{9}(p-q)(2q-p) (2) 29(q−p)(2p−q)\frac{2}{9}(q-p)(2p-q) (3) 29(q−2p)(2q−p)\frac{2}{9}(q-2p)(2q-p) (4) 29(2p−q)(2q−p)\frac{2}{9}(2p-q)(2q-p)

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