Polynomials Worksheet Page 5
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58-7 The Fundamental Theorem of Algebra
Exercises
Quick Review
The Fundamental Theorem of Algebra states that if P (x)
Find the number of roots for each equation.
is a polynomial of degree n, where n Ú 1, then P (x) = 0 has
66. x
3
- 2x + 5 = 0
exactly n roots. This includes multiple and complex roots.
67. 2 - x
4
+ x
2
= 0
68. -x
5
- 6 = 0
Example
4
- 7x
6
+ 2x
3
+ 8x
2
+ 4x - 11 = 0
69. 5x
Use the Fundamental Theorem of Algebra to determine the
number of roots for x
+ 2x
- 3 = 0.
4
2
Find all the zeros for each function.
Because the polynomial is of degree 4, it has 4 roots.
70. P (x) = x
3
+ 5x
2
- 4x - 2
71. P (x) = x
4
- 4x
3
- x
2
+ 20x - 20
72. P (x) = 2x
3
- 3x
2
+ 3x - 2
73. P (x) = x
4
- 4x
3
- 16x
2
+ 21x + 18
383
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