To find out a discriminant, we use b squared – 4ac. If the discriminant is positive, we have 2 roots. If it is 0, we have 1 root. If it is negative, we have no roots. Additionally, if the positive discriminant is rational, both the roots are rational too. If it’s not, they are irrational. We can find the discriminant by using the quadratic formula as well.
Example: ax squared + bx + c
if we wanted to find the discriminant, we’d do b squared – 4ac.
2x squared + 3x + 1
9 – 4(2 x 1) = 9 – 8 = 1. The discriminant is positive, so this equation has 2 roots.