If a,b,c∈R and a+b+c=0, the the quadratic equation 4ax2+3bx+2c=0 has

Let D be the discriminant of the given quadratic. Then      D=9b2−32ac⇒ D=9(−a−c)2−32ac              [∵a+b+c=0]⇒ D=9a2+9c2−14ac⇒ D=c29ac2−14ac+9=c23ac−732+329>0Hence, the roots are real.