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 ?

math  MathMate, Sunday, June 26, 2011 at 11:41am
"Let α, β be the roots of the equation x2  px + r = 0"
This implies:
(xα)(xβ)=0
or
r=αβ ...(1)
p=α+β ...(2)
"and α/2, 2β be the roots of the equation x2  qx + r = 0."
implies:
(xα/2)(x2β)=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