Question

If a+b+c= 0 , then the roots of the equation
4 ax^2 + 3bx + 2c = 0 are​

Answer 1

4ax^2 + 3bx + 2c = 0

Discriminant, Δ=(3b)2−4(4a)(2c)

 Δ=9b2−32ac

 Δ=9(a2+c2+2ac)−32ac

 Δ=9(a2+c2+2ac)−32ac

 Δ=9a2+9c2+18ac−32ac

 Δ=9a2+9c2−14ac

 Δ=7(a2+c2−2ab)+2(a2+c2)

 Δ=7(a−c)2+2(a2+c2)

clearly, (a−c)2>0 & a2+c2>0  ∀ a,c∈R

thus, Δ>0.

Then equation has real roots.