Mathematics - Quadratic Equation Question with Solution | TestHub

$$b{x}^2+cx+a=0$$ Roots are imaginary $\Rightarrow c^2-4ab<0\Rightarrow c^2<4ab\Rightarrow -c^2>-4ab$ $3b^2{x}^2+6bcx+2c^2$ since $3b^2>0$ Given expression has minimum value Minimum value $=\frac{4\left(3b^2\right)\left(2c^2\right)-36b^2{c}^2}{4\left(3b^2\right)}=-\frac{12b^2{c}^2}{12b^2}=-c^2>-4ab$.