If a+b+c=0 then the roots of the equation 4ax2+3bx+2c=0 where a,b,c∈R are

For given equation 4ax2+3bx+2c=0 we have D=(3b)2−4(4a)(2c)=9b2−32ac=9(−a−c)2−32ac=9a2−14ac+9c2=9c2ac2−149ac+1=9ac−792−4981+1which is always positive Hence roots are real and distinct