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AIEEE 2007

JEE Main 2007 Mathematics question on Complex Numbers and Quadratic Equations

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

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