Question

Let $f\left(x\right)=a{x}^2-bx+c^2,b\ne 0$ and $f\left(x\right)\ne 0$ for all $x\in R$. Then

• A. $a+c^2$ $<$ $b$
• B. $4a+c^2>2b$
• C. $9a+c^2<3b$
• D. None of the above.

Answer 1

The correct option is B $4a+c^2>2b$

$f\left(x\right)\ne 0forallx\in R\therefore discriminantislessthanzero{ax}^2-bx+c^2=0b^2-4{ac}^2<0\therefore a>0sof\left(x\right)>0\forall x\in Rf\left(2\right)=4a-2b+c^2>0\therefore 4a+c^2>2b$