If one root of x² + px + q = 0 may be the square of the other, then p^3+q^2 +q=​

1 thought on “If one root of x² + px + q = 0 may be the square of the other, then p^3+q^2 +q=​”

1. Let root of the given equation x

   2

   +px+q=0 are α and α

   2

   Then, we have α⋅α

   2

   =α

   3

   =q and α+α

   2

   =−p

   On cubing both sides, we get

   α

   3

   +(α

   2

   )

   3

   +3α.α

   2

   (α+α

   2

   )=−p

   3

   ⇒q+q

   2

   +3q(−p)=−p

   3

   ⇒p

   3

   +q

   2

   +q(1−3p)=0

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