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

The discriminants of the given equations are    D1=a2+12bD2=c2−4b and D3=d2−8b∴ D1+D2+D3=a2+c2+d2≥0Hence, at least one of D1, D2, D3 is non-negative. Therefore,the equation has at least two real roots.