Download Holt McDougal Algebra 2

Fundamental Theorem of Algebra
• How do we use the Fundamental
Theorem of Algebra and its corollary to
write a polynomial equation of least degree
with given roots?
• How do we identify all of the roots of a
polynomial equation?
Holt McDougal Algebra 2
Fundamental Theorem of Algebra
Using the Fundamental Theorem of Algebra, you
can write any polynomial function in factor form.
To find all roots of a polynomial equation, you can
use a combination of the Rational Root Theorem,
the Irrational Root Theorem, and methods for
finding complex roots, such as the quadratic
formula.
Holt McDougal Algebra 2
Fundamental Theorem of Algebra
Example 1: Finding All Roots of a Polynomial
4
3
2
Solve x – 3x + 5x – 27x – 36 = 0 by finding all roots.
The polynomial is of deg. 4, so there are four roots for the equation.
 1,  2,  3,  4,  6,  9,  12,  18,  36
 1 1  3 5  27  36
4
 1  4  9  36
9
0 36
4
0
0
x 9  0
2
x  9
x    9   3i ,  1 , 4
2
Holt McDougal Algebra 2
Fundamental Theorem of Algebra
Example 2: Finding All Roots of a Polynomial
4
3
2
Solve x + 4x – x +16x – 20 = 0 by finding all roots.
The polynomial is of deg. 4, so there are four roots for the equation.
 1,  2,  4,  5,  10,  20
1 1 4  1 16  20
5
1
5
4
0  240
5
20
0
0
x 40
2
x  4
x    4   2i , 1 ,  5
2
Holt McDougal Algebra 2
Fundamental Theorem of Algebra
Lesson 4.2 Practice B
Holt McDougal Algebra 2