Untitled.notebook
November 13, 2015
Do Now: Solve the following by quadratic formula:
2x 2 + 2x +5 = 0
using the Untitled.notebook
November 13, 2015
Untitled.notebook
November 13, 2015
Number and Nature of the Roots
of a Quadratic Equation
Untitled.notebook
November 13, 2015
What are the possible number of roots a quadratic
equation may have?
• 1
• 2
What are the different types of roots a
quadratic equation may have?
• real ( ± 2, 2 ±√3)
• complex ( 3 ±i, -2±3i)
Is it possible to determine whether or not roots are real or imaginary without evaluating the entire quadratic formula? (i.e. actually finding the roots?)
is called the discriminant
b2 ­4ac
is called the discriminant
If b2­4ac = 0 then there is 1 real root (with multiplicity 2)
If b2­4ac > 0 then there are 2 real roots
If b2­4ac < 0 then there are 2 complex roots (conjugates)
Untitled.notebook
November 13, 2015
b2 ­4ac
<0
=0
2 complex
roots
1 real
root
>0
2 real
roots
Determine the number and nature of the roots of the following equations.
1) 9x
2
-6x+1=0
4) -x
2
-3=0
2) x
5) 2x
2
2
-4x+13=0
+5x-12=0
3) x2-6x+9=0
6) -x
2
+3x+11=0
Untitled.notebook
November 13, 2015
If a quadratic equation has imaginary roots, where will
the equation intercept the x-axis?
Previously, we determined that the following
equations have complex roots. Graph them on your
calculator and look for similarities.
x 2 -4x+13=0
-x 2 -3=0
Conclusion: If the discriminant is < 0, then the graph
of the equation will intercept the x - axis at exactly
______ point(s).
If a quadratic equation has 1 real root, where will the
equation intercept the x-axis?
Previously, we determined that the following
equations have 1 real root. Graph them on your
calculator and look for similarities.
x 2 -6x+9=0
9x 2 -6x+1=0
Conclusion: If the discriminant is =0, then the graph
of the equation will intercept the x - axis at exactly
______ points.
Untitled.notebook
November 13, 2015
If a quadratic equation has 2 real roots, where will the
equation intercept the x-axis?
Previously, we determined that the following
equations have 2 real roots. Graph them on your
calculator and look for similarities.
2x 2 +5x-12=0
-x 2 + 3x+11=0
Conclusion: If the discriminant is > 0, then the graph
of the equations will intercept the x - axis at exactly
______ points.
Example
Discriminant
b2-4ac
Number and
nature of the
roots
2 complex
1 real
2 real
Graph
Untitled.notebook
November 13, 2015
Homework: Discrimant Worksheet