Theory of Equations 1 Question 22

23. Let α,β be the roots of the equation x2−px+r=0 and α2,2β be the roots of the equation x2−qx+r=0. Then, the value of r is

(2007,3M)

(a) 29(p−q)(2q−p)

(b) 29(q−p)(2p−q)

(c) 29(q−2p)(2q−p)

(d) 29(2p−q)(2q−p)

Show Answer

Answer:

Correct Answer: 23. (d)

Solution:

  1. The equation x2−px+r=0 has roots α,β and the equation x2−qx+r=0 has roots α2,2β.

⇒r=αβ and α+β=p

and α2+2β=q⇒β=2q−p3 and α=2(2p−q)3

⇒αβ=r=29(2q−p)(2p−q)

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