Question

if the sum of the roots of ax^2+2x+3a=0 is equal to their products then a= ??

Answer 1

Let α and β are the roots of ax²+2x+3a=0

So sum of the roots = α+β = -(coeff. of x)/(coeff. of x²) = -2/a      ...(1)

And product of the roots = αβ = (constant term)/(coeff. of x²) = 3a/a = 3        ...(2)

According the the question  

sum of the roots = product of the roots

-2/a = 3                                                              [ using (1)  and (2) ]

⇒ a = -2/3