# How do you find the discriminant x^2+2x-1?

Mar 20, 2018

See a solution process below:

#### Explanation:

The quadratic formula states:

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 $\textcolor{red}{a}$

$\textcolor{b l u e}{2}$ for $\textcolor{b l u e}{b}$

$\textcolor{g r e e n}{- 1}$ for $\textcolor{g r e e n}{c}$

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

$4 - \left(- 4\right) \implies$

$4 + 4 \implies$

$8$

Therefore, this quadratic would have two real solutions.