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]}