# How do you find the value of the discriminant and determine the nature of the roots 4a^2=8a-4?

##### 1 Answer
Apr 2, 2018

See a solution process below:

#### Explanation:

First, put this equation in standard quadratic form:

$4 {a}^{2} = 8 a - 4$

$4 {a}^{2} - \textcolor{red}{8 a} + \textcolor{b l u e}{4} = 8 a - \textcolor{red}{8 a} - 4 + \textcolor{b l u e}{4}$

$4 {a}^{2} - 8 a + 4 = 0 - 0$

$4 {a}^{2} - 8 a + 4 = 0$

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:

$\textcolor{red}{4}$ for $\textcolor{red}{a}$

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

$\textcolor{g r e e n}{4}$ for $\textcolor{g r e e n}{c}$

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

$64 - 64 \implies$

$0$

Because the discriminate is $0$ there will be just one solution or one root.