Determine the discriminant for the given equation x^2+4x+5=0. Then describe the roots (how many and what type).

Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c

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

= 16 - 20

= - 4

-4 < 0, therefor there are no roots

(If the discriminant = 0, then there is one root

If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots

If the discriminant < 0, there are no roots)