Question

The sum of the two roots of the equation x^3+a1x^2+a2x+a3=0,is zero.Prove that a1a2-a3=0​

Answer 1

Given equation is x

3+ax 2+bx+c=0

Let the roots be α,−α,β

Then α−α+β=−a

⇒β=−a ....(1)

Also, −α 2+αβ−αβ=b⇒−α 2=b (2)Also, −α 2β=−c ....(by (1)and (2))

⇒−ab=−c

⇒ab=c

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