Question

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?

Answer 1

Discriminant = `-215`
Therefore, there are two imaginary solutions.

Explanation:

First, you must take the given equation and move it around to become `ax^2+bx+c =0` format.

To do this, you must start off my subtracting `3x` from both sides. You're left with:

`10x^2-5x+2=-4`

Now you add 4 to both sides.

`10x^2-5x+6=0`

Now, the formula to find the discriminant is: `Delta = b^2-4ac`
Using this equation, plug in what you have.

a = 10 b = -5 c = 6

Thus, you should have: `Delta =(-5)^2-4(10)(6)`

Your answer equals: `Delta =-215`

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 `-215 < 0,` you will have 2 imaginary solutions.

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]}