Question

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

Answer 1

Answer:Either -1 or, 5

Step-by-step explanation:

x²-4x-5=0

x²-5x+x-5=0

(x+1)(x-5)=0

Either x=-1 or, x=5

Answer 2

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

Step-by-step 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).