Relation between Roots and Coefficients for Quadratic
Let α, β be t...
Question
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
A
29(p−q)(2q−p)
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B
29(q−p)(2p−q)
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C
29(q−2p)(2q−p)
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D
29(2p−q)(2q−p)
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Solution
The correct option is D29(2p−q)(2q−p) As α,β are the roots of x2−px+r=0 ∴α+β=p .......(1) and αβ=r .......(2) Also α2,2β are the roots of x2−qx+r=0 ∴α2+2β=q or α+4β=2q .....(3) Solving (1) and (3) for αandβ,we get β=13(2q−p) and α=23(2q−q) Substituting values of α and β, in equation (2), we get 29(2p−q)(2q−p)=r.