Question

For the expression f(x) = a $x^2$ + bx + c (a > 0), having both real roots, the condition for both real roots to be greater than a real value $x_0$ is

• A. f( ) > 0, < ( )
• B. f( ) < 0, ≥ ( )
• C. f( ) ≥ 0, < ( )
• D. f( ) > 0, = ( )

Answer 1

The correct option is A

f( ) > 0, < ( )

As a > 0, graph is cup shaped parabola

Consider the graph of f(x) in which roots of f(x) is shown to be greater than $x_0$ .

We know f($x_0$ ) > 0

Now, for $x_0$ to be on left of $\alpha$, & $\beta$, and also f($x_0$ ) > 0, we can comfortably take $x_0$ < ( $\frac{-b}{2a}$)

So, A is right option.