Question

If the roots of the equation $b{x}^2+cx+a=0$be nonreal, then for all real values of x, the expression $3b^2{x}^2+6bcx+2c^2$ is

• A. less than 4ab
• B. greater than – 4ab
• C. less than – 4ab
• D. greater than 4ab

Answer 1

The correct option is A

less than 4ab

$\text{roots of}b{x}^2+cx+a=0.\text{are non real}\Rightarrow c^2-4ab<0\Rightarrow c^2<4ab\Rightarrow -c^2>-4ab3b^2{x}^2+6bcx+2c^2\text{Min:Value}=\frac{4\left(3b^2\right)\left(2c^2\right)-36b^2{c}^2}{4.\left(3b^2\right)}=\frac{-12b^2{c}^2}{12b^2}=-c^2>-4ab$