SOLUTION: If one root of the equation x^2+px+q=0 is twice of the second root, then prove that 2p^2=9q.

SOLUTION: If one root of the equation x^2+px+q=0 is twice of the second root, then prove that 2p^2=9q.

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Question 1013673: If one root of the equation x^2+px+q=0 is twice of the second root, then prove that 2p^2=9q.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
quadratic formula
x=(1/2)(-p+sqrt(p^2-4q)) and that is 2*(1/2) (-p-sqrt (p^2-4q))
multiply both sides by 2
-p+sqrt(p^2-4q)=2*(-p-sqrt(p^2-4q))
-p+sqrt(p^2-4q)=-2p-2sqrt(p^2-4q)
p=-3 sqrt(p^2-4q)
square both sides
p^2=9 (p^2-4q)=9p^2-36q
-8p^2= -36 q
2p^2=9q

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