Download 9.6 The Discriminant

Algebra
9.6
The Discriminant
The Discriminant
In the quadratic formula, the expression
inside the radical is the discriminant.
- b +-√ b² - 4ac
x=
2a
The discriminant can be used to find the number
of solutions a quadratic equation has.
Before using Quadratic
Formula to solve…….
Compute the value of
b²- 4ac
If the value is:
POSITIVE
There are 2 solutions
ZERO
There is 1 solution
NEGATIVE
There are no real solutions
How b²- 4ac effects the
Quadratic Formula
± 16
±4
POSITIVE
numbers have
2 square
roots
2 solutions
± 0
=0
ZERO has 1
square root
1 solution
± -25
not possible
NEGATIVE
numbers don’t
have square
roots
no real solutions
Try it with these equations
Compute the value of
x²- 3x – 4 = 0
b²- 4ac
(-3)²- 4(1)(-4) = 9 + 16 = 25
positive, 2 solutions
-x²+ 2x – 1 = 0 (2)²- 4(-1)(-1) = 4 - 4 = 0
zero, 1 solution
2x²- 2x + 3 = 0 (-2)²- 4(2)(3) = 4 - 24 = -20
negative, NO solutions
The number of solutions tells you what the related
parabola looks like.
CROSSER
2 solutions
TOUCHER
1 solution
2 x-intercepts 1 x-intercept
FLOATER/SINKER
no solution
no x-intercepts
Homework
pg. 544 # 1-20