If a,b,c,d∈R then the equation x2+ax−3bx2−cx+ b) x2−dx+2b=0 has

The discriminants of the three factors are, D1=a2+12b;D2=c2−4b and D3=d2−8b∴ D1+D2+D3=a2+c2+d2≥0 i.e., at least one of D1,D2,D3 is non-negative.  Hence, the equation has at least two real roots.