Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 - 4x - 5 = 0

Discriminant is 36. There are two real solutions (both different)

Explanation:

The equation 1x^2 - 4x - 5 = 0 is in the form ax^2 + bx + c = 0. We see that

a = 1, b = -4, c = -5

So the discriminant is

D = b^2 - 4ac

D = (-4)^2 - 4(1)(-5)

D = 16 + 20

D = 36 is the discriminant

The discriminant is positive, so there are two different solutions. The solutions are both real.

note: because the discriminant is a perfect square, this means that the two solutions are rational (ie fractions of whole numbers).

the answer is 5636.7