For the expression f(x) = a $x^{2}$ + bx + c (a < 0), $b^{2}$ > 4ac always. A real value $x_{0}$ will lie in between the real roots of f(x) if

f() < 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f() > 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

f() = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Can't say

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
f() > 0

As a < 0, graph of f(x) will be downward parabola .

Let us visualize through the graph

Let $α$ , $β$ be the roots.

If we take any value $x_{0}$ on x-axis in between $α$ $&$ $β$ , from the graph we can observe that f( $x_{0}$ ) > 0

So, f( $x_{0}$ ) > 0 is the condition required.

Suggest Corrections

Similar questions

For the expression f(x) = a $x^{2}$ + bx + c (a > 0), $b^{2}$ > 4ac always. A real value $x_{0}$ will lie in between the roots of f(x) if

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

One or more options can be correct:

The condition for the roots of the quadratic equation f(x)= a $x^{2}$ +bx+c to be less than a real value x₀ is/are

For the expression f(x) = a $x^{2}$ + bx + c, (a > 0), the condition for both real roots of f(x) to be greater than (or) lesser than a real value M is,

Q. If both f(x) and g(x) are differentiable functions at

x = x_{0}

, then the function defined as h(x) = maximum {f(x), g(x)} :

Join BYJU'S Learning Program

For the expression f(x) = a x2 + bx + c (a < 0), b2 > 4ac always. A real value x0 will lie in between the real roots of f(x) if

The correct option is B f() > 0 As a < 0, graph of f(x) will be downward parabola . Let us visualize through the graph Let α, β be the roots. If we take any value x0 on x-axis in between α & β, from the graph we can observe that f(x0) > 0 So, f(x0) > 0 is the condition required.

For the expression f(x) = a $x^{2}$ + bx + c (a < 0), $b^{2}$ > 4ac always. A real value $x_{0}$ will lie in between the real roots of f(x) if