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Question

If one root of equation x2px+q=0 is twice the other then prove that 2p2=9q

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Solution

Let ß is one root and 2ß is 2nd root
x2px+q=0 so,
The sum of the roots=P
ß+2ß=P
ß=P3 ---(1)
The product of the roots =q
2ß.ß=q
2ß2=q
put eqn (1)
2(P3)2=q
2P2=9q

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