The Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra
November 06, 2017
The Fundamental Theorem of Algebra
Nov 68:13 AM
1
The Fundamental Theorem of Algebra
November 06, 2017
Objectives: Use the fundamental theorem of Algebra to determine numbers of zeros of polynomial functions Find rational zeros of polynomial functions Find complex zeros
Nov 68:14 AM
2
The Fundamental Theorem of Algebra
November 06, 2017
The Fundamental Theorem of Algebra
If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system
The degree of a polynomial tells you exactly how many zeros that you will have.
Nov 68:15 AM
3
The Fundamental Theorem of Algebra
November 06, 2017
The Rational Zero Test
If you have a polynomial that has integer coefficients, then every rational zero of f has the form of Rational Zero = Where p and q have no common factors other than q and p is a factor of the constant term and q is a factor of the lead term.
Nov 68:16 AM
4
The Fundamental Theorem of Algebra
November 06, 2017
Example: Find the rational zeros of f(x) = x4 x3 + x2 3x 6
Nov 68:19 AM
5
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:50 AM
6
The Fundamental Theorem of Algebra
November 06, 2017
Find the rational zeros of f(x) = x3 15x2 + 75x 125
Nov 68:20 AM
7
The Fundamental Theorem of Algebra
November 06, 2017
Nov 612:23 PM
8
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:58 AM
9
The Fundamental Theorem of Algebra
November 06, 2017
When the leading coefficient of a polynomial is not 1, the number of possible rational zeros can increase dramatically. In such cases, the search can be shorten in several ways, but the easiest way is to graph the function.
Nov 68:21 AM
10
The Fundamental Theorem of Algebra
November 06, 2017
Find the rational zeros of f(x) = 2x3 + 3x2 8x + 3
Nov 68:22 AM
11
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:26 AM
12
The Fundamental Theorem of Algebra
November 06, 2017
Find the rational zeros of f(x) = 10x3 + 15x2 + 16x 12
Nov 68:26 AM
13
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:27 AM
14
November 06, 2017
The Fundamental Theorem of Algebra
Nov 68:13 AM
1
The Fundamental Theorem of Algebra
November 06, 2017
Objectives: Use the fundamental theorem of Algebra to determine numbers of zeros of polynomial functions Find rational zeros of polynomial functions Find complex zeros
Nov 68:14 AM
2
The Fundamental Theorem of Algebra
November 06, 2017
The Fundamental Theorem of Algebra
If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system
The degree of a polynomial tells you exactly how many zeros that you will have.
Nov 68:15 AM
3
The Fundamental Theorem of Algebra
November 06, 2017
The Rational Zero Test
If you have a polynomial that has integer coefficients, then every rational zero of f has the form of Rational Zero = Where p and q have no common factors other than q and p is a factor of the constant term and q is a factor of the lead term.
Nov 68:16 AM
4
The Fundamental Theorem of Algebra
November 06, 2017
Example: Find the rational zeros of f(x) = x4 x3 + x2 3x 6
Nov 68:19 AM
5
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:50 AM
6
The Fundamental Theorem of Algebra
November 06, 2017
Find the rational zeros of f(x) = x3 15x2 + 75x 125
Nov 68:20 AM
7
The Fundamental Theorem of Algebra
November 06, 2017
Nov 612:23 PM
8
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:58 AM
9
The Fundamental Theorem of Algebra
November 06, 2017
When the leading coefficient of a polynomial is not 1, the number of possible rational zeros can increase dramatically. In such cases, the search can be shorten in several ways, but the easiest way is to graph the function.
Nov 68:21 AM
10
The Fundamental Theorem of Algebra
November 06, 2017
Find the rational zeros of f(x) = 2x3 + 3x2 8x + 3
Nov 68:22 AM
11
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:26 AM
12
The Fundamental Theorem of Algebra
November 06, 2017
Find the rational zeros of f(x) = 10x3 + 15x2 + 16x 12
Nov 68:26 AM
13
The Fundamental Theorem of Algebra
November 06, 2017
Nov 68:27 AM
14
