# How do you find the discriminant of #10x^2-2x+2=3x-4# and use it to determine if the equation has one, two real or two imaginary roots?

##### 1 Answer

Discriminant =

Therefore, there are two imaginary solutions.

#### Explanation:

First, you must take the given equation and move it around to become

To do this, you must start off my subtracting

Now you add 4 to both sides.

Now, the formula to find the discriminant is:

Using this equation, plug in what you have.

**a** = 10 **b** = -5 **c** = 6

Thus, you should have:

Your answer equals:

Here is a key to find out the type of answer you'll receive.

- If the discriminant:
#Delta < 0# you will have 2 imaginary solutions. - If the discriminant:
#Delta = 0# , you will have one real answer. - If the discriminant:
#Delta > 0,# you will have two real solutions.

Because

You can even check a graph and see that because the parabola never touches the x-axis, there are no real solutions, but two imaginary:

graph{10x^2-5x+6 [-16.05, 16.04, -8.03, 8.02]}