if one root of the equation x2 - px +q =0 twice the other then show that 2p2 =9q
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let ß is one root
and 2ß is 2nd root
x² -px + q = 0
so,
sum of roots = P
ß + 2ß = P
ß = P/3 ---(1)
product of roots = q
2ß.ß = q
2ß² = q
put eqn (1)
2(P/3)² = q
2P² = 9q
and 2ß is 2nd root
x² -px + q = 0
so,
sum of roots = P
ß + 2ß = P
ß = P/3 ---(1)
product of roots = q
2ß.ß = q
2ß² = q
put eqn (1)
2(P/3)² = q
2P² = 9q
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