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?
See a solution process below:
First, we need to put the equation in standard form. Subtract
The quadratic formula states:
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.
We now have the form:
The discriminant of a quadratic is:
Hope this helps.