2. 7.5 Zeros of Polynomial Functions
Objectives: Use the Rational Root Theorem and the Complex Conjugate Root Theorem. Use the Fundamental Theorem to write a polynomial function.
Standard: N. Solve equations both symbolically and graphically.

3. The Rational Root Theorem can be used to identify possible roots of
polynomial equations with integer coefficients.
Rational Root Theorem
Let P be a polynomial function with integer coefficients in standard form.
If p/q (in lowest terms) is a root of P(x) = 0, then
p is a factor of the constant term of P and
q is a factor of the leading coefficient of P.

7. * 8x3 + 10x2 - 11x + 2 = 0

9. * Q(x) = x3 - 6x2 + 7x + 2

10. * Q(x) = x3 + 4x2 – 6x – 12

11. Ex 3. Find all of the zeros of: Same as above, but you will get an imaginary #.
* P(x) = 3x 3 – 10x x – 4

12. * P(x) = x3 - 9x2 + 49x – 145

13. * P(x) = -4x 3 + 2x2 – x + 3

14. Complex Conjugate Root Theorem
If P is a polynomial function
with real-number
coefficients and a + bi
(where b ≠ 0) is a root of P(x) = 0,
then a – bi is also a root of P(x) = 0.

16. Fundamental Theorem of Algebra: Every polynomial function of degree n ≥ 1 has at least one complex zero
Corollary: Every polynomial function of degree
n ≥ 1 has exactly n complex zeros, counting multiplicities.

18. Writing Activities

19. PSSA Warm-Up Question Algebra II Chp 7
Standard S Analyze linear, polynomial, and rational functions.
How can you identify and describe functions and their graphs? What are the functions zero(s)?
1). Linear Function y = ½x + 2
2). Quadratic Function y = x2 – 2x – 3
3). Cubic Function y = x3 – 4x

20. Review of Zeros of Polynomial Functions

22. Homework
Integrated Algebra II- Section 7.5 Level A
Honors Algebra II- Section 7.5 Level B