Discriminant

(b^2-4ac) tells the number of REAL and/or UNIQUE solutions.

b^2-4ac > 0, we have 2 distinct, real solutions

b^2-4ac = 0, there is 1 real solution (double root)

b^2-4ac < 0, there are 0 real solutions

Ex. Find the discriminant of each equation, then, determine the number of real solutions.

a. 2x^2+4x+1=0

ax^2+bx+c

a=2,b=4,c=1

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

16-8=8

2 real solutions.

b. 2x^2+4x+2=0

ax^2+bx+c

a=2,b=4,c=2

(4)^2-4(2)(2)

16-16=0

There is 1 real solution

c. 2x^2+4x+3=0

ax^2+bx=c

a=2,b=4,c=3

(4)^2-4(2)(3)

16-24=-8

There are 0 real solutions