Question

If a, b, c $ϵ$ R and a $\ne$ 0, c > 0, the graph of $f\left(x\right)$ = $a{x}^2+bx+c$ for which $f\left(x\right)=0$ has only imaginary roots, will look like

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given $f\left(x\right)$ = $a{x}^2+bx+c$ has imaginary roots

$\Rightarrow$ D < 0

$b^2-4ac$ < 0

$b^2$< 4ac

As b $ϵ$ R, $b^2$ is always > 0 and for 4ac > $b^2$, 4ac should be > 0

$\Rightarrow$ a & c should have same sign

As c > 0, a> 0

Hence as a > 0 and D < 0, graph is bowl shaped and don't touch x-axis $\Rightarrow$ f(x) is always positive.

So, A is right option