Quadratic Equation

If one root is square of the other root of the equation x²+px+q=0, then find the relation between p and q.

Expert Solution

Let α and α² be the two roots of the equation x²+ px+q = 0.

Therfore,now we have α + α² = -p

Taking α common

α(1+α) = -p,

and α³ = q

Now, (α(1+α)³ = (-p)³

α³(1+α)³ = -p³

⇒α³ [1+α³+3α(1+α)]=−p³

⇒q[1+q−3p]=−p³

⇒p³ −(3p−1)q+q² =0, which is the relation between p and q.

Relation between p and q = p3 −(3p−1)q+q2 =0

Nikhil Thakur answered 2 years ago

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