# How to use the discriminant to find out how many real number roots an equation has for x^2 - 8x + 3 = 0?

Jun 3, 2018

See a solution process below:

#### Explanation:

For $a {x}^{2} + b x + c = 0$, the values of $x$ which are the solutions to the equation are given by:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

The discriminate is the portion of the quadratic equation within the radical: ${\textcolor{b l u e}{b}}^{2} - 4 \textcolor{red}{a} \textcolor{g r e e n}{c}$

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

$\textcolor{red}{1}$ for $\textcolor{red}{a}$

$\textcolor{b l u e}{- 8}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{3}$ for $\textcolor{g r e e n}{c}$

${\textcolor{b l u e}{- 8}}^{2} - \left(4 \cdot \textcolor{red}{1} \cdot \textcolor{g r e e n}{2}\right) \implies 64 - 8 \implies 56$

$56$ is positive therefore you would get two real solutions.