Question

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

Answer 1

Answer:

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Answer 2

Given equation is x

3+ax 2+bx+c=0

Let the roots be a,-a,ß

Then a-a+B=-a

⇒ B=-a

.... (1)

Also, -a 2 + aß-aß = b⇒-a 2 = b

(2)Also,

-a 2B=-c ...(by (1)and (2))

⇒-ab = -c

⇒ab=c

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