Alg II 5­6 The Fundamental Theorem of Algebra ­ End.notebook
November 02, 2016
5-6 The Fundamental Theorem of Algebra
The degree of a polynomial equation tells you how many roots the equation has.
Factors:
0 = (x + 2)(x −2)
0 = (x −1)(x −1)
0 = (x + 1 + i)(x + 1 − i)
Ex. 1 Find the number of complex roots for each equation.
A.
2x4 − x3 + 2x2 + 5x − 26 = 0
B.
4x6 − x5 − 24 = 0
C.
− 12 + x + 10x2 + 3x3 = 0
1
Alg II 5­6 The Fundamental Theorem of Algebra ­ End.notebook
November 02, 2016
Ex. 2 Find all the roots of the equation.
x5 − x4 − 3x3 + 3x2 − 4x + 4 = 0
Ex. 3 Find all the zeros of the equation.
x4 + 2x3 = 13x2 − 10x
2
Alg II 5­6 The Fundamental Theorem of Algebra ­ End.notebook
November 02, 2016
Ex. 4 Find all the roots of the equation. x4 + x3 − 7x2 − 9x − 18 = 0?
3