1. Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts
L6-5 and L6-6
Obj: Students will find rational roots.
Obj: Students will use the Fundamental Theorem of Algebra to solve polynomials
Important Terms
Rational Numbers
Irrational Numbers
Fundamental Theorem of Algebra
Roots/Zeros/X-Intercepts
Rational Root theorem

2. Find the possible rational roots of 3x3 – x2 – 15x + 5 = 0.
Theorems About Roots of Polynomial Equations
Find the possible rational roots of 3x3 – x2 – 15x + 5 = 0.
Then find the rational roots

3. Find the roots of 5x3 – 24x2 + 41x – 20 = 0.

4. Finding Rational Roots 1. x³ + x² - 3x – 3 = 0 Find the roots 2
Finding Rational Roots 1. x³ + x² - 3x – 3 = 0 Find the roots 2. 2x³ - x² + 2x -1 = 0

8. Obj: Students will use the Fundamental Theorem of Algebra to solve polynomials

9. By the corollary to the Fundamental Theorem of Algebra,
LESSON 6-6
Additional Examples
For the equation x4 – 3x3 + 4x + 1 = 0, find the number of complex roots, the possible number of real roots, and the possible rational roots.
By the corollary to the Fundamental Theorem of Algebra,
x4 – 3x3 + 4x + 1 = 0 has four complex roots.
By the Imaginary Root Theorem, the equation has either no imaginary roots,
two imaginary roots (one conjugate pair), or four imaginary roots
(two conjugate pairs). So the equation has either zero real roots,
two real roots, or four real roots.
By the Rational Root Theorem, the possible rational roots of the
equation are ±1.

10. Find the number of complex zeros of ƒ(x) = x5 + 3x4 – x – 3.
The Fundamental Theorem of Algebra
Find the number of complex zeros of ƒ(x) = x5 + 3x4 – x – 3.
Find all the zeros.

11. Find all the zero’s
f(x) = x³ + x² -x + 2
y = x³ - 2x² + 4x - 8

12. Homework
6.5 (p 345) #2-24e
6.6 (p 349) #10-16e 22-26e 32