2015/16 TI-Smartview 2.5 The Fundamental Theorem of Algebra.
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Transcript of 2015/16 TI-Smartview 2.5 The Fundamental Theorem of Algebra.
2015/16TI-Smartview
2.5 The Fundamental
Theorem of Algebra
HWQ
2 52 2
ii i
Perform the operation and simplify. Work must be shown to receive
credit.
2.5 The Fundamental Theorem of Algebra
Students will find all zeros of polynomial functions, including complex zeros.
Students will find conjugate pairs of complex zeros.
Students will find zeros of polynomials by factoring.
The Fundamental Theorem of Algebra
If f(x) is a polynomial of degree n, then f(x) has n zeros, real and (or) imaginary.
Example 1: Real Zeros of a Polynomial Function
Counting multiplicity, justify that the second-degree polynomial function has exactly two factors and zeros.
f x x x( ) 2 6 9
Example 2: Real and Imaginary Complex Zeros of a Polynomial Function
Justify that the third degree polynomial functionhas exactly three factors and zeros.
f x x x( ) 3 4
Example 3: Finding the zeros of a Polynomial Function
Write as the product of linear factors, and list all the zeros of f.
f x x x x x( ) 5 3 22 12 8
Example 4: Finding a Polynomial with Given Zeros
Find a fourth degree polynomial function with real coefficients that has - 1, - 1, and 3i as zeros.
• Find all zeros without graphing the polynomial first given is a zero:
1 3i
4 3 23 6 2 60x x x x
Example 4: More practice
Example 5: Factoring a PolynomialFor the following polynomial list all zeros.
f x x x( ) 4 2 20
You try:
• Solve by factoring: 4 2 2 0x x
• Solve: 4 3 23 5 21 22 0x x x x
Example 6: More practice
Homework
2.5 pg. 140 #9-35 odd, 45, 47, 57
**QUIZ TOMORROW OVER SECTIONS 2.4 & 2.5**