1. Warm Up Identify all the real roots of each equation.
1. 4x5 – 8x4 – 32x3 = 0
0, –2, 4
2. x3 –x2 + 9 = 9x
1, –3, 3
3. x = 17x2
–1, 1, –4, 4
4. 3x3 + 75x = 30x2
0, 5

2. 6-8 Roots and Zeros – Day 1 SWBAT
determine the number and type of roots for a polynomial equation.
Find the zeros of a polynomial function.
Holt McDougal Algebra 2
Holt Algebra 2

3. Notes: - pg 362

4. Graphs of an Equation Zeros: x = -2, -1, 1, 2 Factors:
List the factors and zeros of
the graph.
Zeros:
x = -2, -1, 1, 2
Factors:
(x + 2)(x + 1)(x – 2)(x – 1)

5. Determine the number of roots.
x2 – 8x + 16 = 0
x = 4  double root
One real repeated root
4 has a multiplicity of 2
x4 – 1 = 0
x = + i , + 1
Two real roots, 2 imaginary roots

6. Try on your own:
Pg # 1A, 1B

7. Notes:
Notice that the degree of the function is the same as the number of zeros. This is true for all polynomial functions. However, all of the zeros are not necessarily real zeros. Polynomials functions, like quadratic functions, may have complex zeros that are not real numbers.
For example:
2x2 + 4x + 1 has 2 roots
3x4 + 1 has 4 roots

8. PARCC Question
If m is a constant, what is the value of ‘m’ such that the polynomial m2x3 – 4mx + 4 is divisible by x - 1? What type of root is it?

9. HOMEWORK
Pg 366
#11-16 all

10. Warm Up
#79. Write a system of equations, do not solve.
DO NOW

11. 6-8 Roots and Zeros – Day 2 SWBAT
determine the number and type of roots for a polynomial equation.
Find the zeros of a polynomial function.
Holt McDougal Algebra 2
Holt Algebra 2

12. You have learned several important properties about real roots of polynomial equations.
You can use this information to write polynomial function when given in zeros.

13. Writing Polynomial Functions
Write the simplest polynomial with roots –1 and 4.

14. Write the simplest polynomial function with the given zeros -2, 2, and 4.

15. Use Zeros to Write a Polynomial
Complex Conjugates Theorem:
If a + bi is a zero, then its conjugate is also a zero.
Write a polynomial function with zeros that include 3 and 2i.
(x – 3)(x – 2i)(x + 2i)
Multiply conjugates first (it’s easier)

16. Write the simplest function with zeros 2i and 1 in standard form.

17. Write the simplest polynomial function with the given zeros in standard form.
1. 2, –1, 1
2. 0, –2i
3. 2i, 1, –2

18. Homework