# How do you find the discriminant of #5x^2-4x+1=3x# and use it to determine if the equation has one, two real or two imaginary roots?

##### 2 Answers

See a solution process below:

#### Explanation:

First, we need to put the equation in standard form. Subtract

The quadratic formula states:

For

The discriminate is the portion of the quadratic equation within the radical:

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:

Because the discriminate is **positive**, you will get two real solutions or roots.

See below.

#### Explanation:

Arrange

To get:

We now have the form:

The discriminant of a quadratic is:

if:

if:

if:

Hope this helps.