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
Mar 7, 2017

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]}