# What is the discriminant of 2x^2− x + 8 = 0 and what does that mean?

Jul 16, 2015

The discriminant of $2 {x}^{2} - x + 8 = 0$ is ${\left(- 1\right)}^{2} - 4 \left(2\right) \left(8\right) = - 63$
This tells that there are no Real roots to the given equation.

#### Explanation:

For a quadratic equation in the general form:
$\textcolor{w h i t e}{\text{XXXX}}$$a {x}^{2} + b x = c = 0$
the discriminant is:
$\textcolor{w h i t e}{\text{XXXX}}$${b}^{2} - 4 a c$

The discriminant is a component of the general quadratic formula for solving a quadratic equation:
$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

If the discriminant (${b}^{2} - 4 a c$) is less than zero
then the "solution" requires
$\textcolor{w h i t e}{\text{XXXX}}$the square root of a negative value
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$which does not exist as any Real value,
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$ and therefore there can be no Real solutions to the equation.