Use the discriminant to classify each quadratic equation by the number and type of solutions of the equation

Question

Use the discriminant to classify each quadratic equation by the number and type of solutions of the equation. Fill in the blank using these solutions:

x^2+5x+9=0, x^2-7=3x,0 6x-9-x^2=0, 6x^2=1-x

real solutions imaginary solutions

One solution ____?_____ ____?_____

Two solutions ____?_____ ____?_____

Answer 1

if b^2 - 4ac < 0 then you have two imaginary solutions

if b^2 - 4ac = 0 then you have 1 real solution

if b^2 - 4ac > 0 then you have 2 real solutions

for example, for x^2 + 5x + 9, a = 1, b = 5 and c = 9

b^2 - 4ac = (5)^2 - 4(1)(9) = 25 - 36 = -11, so you have two imaginary solutions.