Posted by **shailja** on Saturday, June 25, 2011 at 5:47am.

1. Let α, β be the roots of the equation x2 - px + r = 0 and α/2, 2β be the roots of the equation x2 - qx + r = 0. Then the value of r is ?

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**MathMate**, Sunday, June 26, 2011 at 11:41am
"Let α, β be the roots of the equation x2 - px + r = 0"

This implies:

(x-α)(x-β)=0

or

r=αβ ...(1)

p=α+β ...(2)

"and α/2, 2β be the roots of the equation x2 - qx + r = 0."

implies:

(x-α/2)(x-2β)=0

or

r=αβ ...(1a)

q=α/2+2β ...(3)

From (2) and (3) solve for α and β in terms of p and q, hence find r=αβ

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