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

x^2 - 4x - 5 = 0

4x^2 + 20x + 25 = 0

All these equations are in the form of ax^2 + bx + c = 0, where a, b, and c are some numbers. the discriminants of equations like this are equal to b^2 - 4ac. if the discriminant is negative, there are two imaginary solutions. if the discriminant is positive, there are two real solutions. if the discriminant is 0, there is one real solution.

x^2 + 4x + 5 = 0

b^2 - 4ac

4^2 - 4 (1) (5)

16-20

-4, two imaginary solutions.

x^2 - 4x - 5 = 0

b^2 - 4ac

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

16 + 20

36, two real solutions.

4x^2 + 20x + 25 = 0

b^2 - 4ac

20^2 - 4 (4) (25)

400 - 400

0, one real solution.