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Transcript Lesson 4.2B

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
0
2
x 9 0
0
4
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
4
5
20
0 240 0
2
x 40
0
5
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