WARM UP
Introduction to Finding all Zeros
EQ: How do we use the Fundamental Theorem of Algebra and it’s corollary to
find the zeros of a polynomial?
Assessment: Students will write a summary on ways to use the Fundamental
Theorem of Algebra to find the zeros of a polynomial.
Key Term
• When a solution appears more than once this
repeated solution
called a _______________.
** Note: For the equation f(x) = 0, k is a repeated
solution if and only if the factor (x – k) has a degree
greater than 1 when f is factored.
EQ: How do we use the Fundamental Theorem of Algebra and it’s corollary to find the zeros of a
polynomial?
Assessment: Students will write a summary on ways to use the Fundamental Theorem of Algebra to
find the zeros of a polynomial.
KEY CONCEPT
>
one
n
2
3
EQ: How do we use the Fundamental Theorem of Algebra and it’s corollary to find the zeros of a
polynomial?
Assessment: Students will write a summary on ways to use the Fundamental Theorem of Algebra to
find the zeros of a polynomial.
Find the number of solutions and zeros
a. How many solutions
does the equation
x3 + 5x2 + 4x + 20 = 0
have?
b. How many zeros does
the function
f (x) = x4 – 8x3 + 18x2 – 27
have?
EQ: How do we use the Fundamental Theorem of Algebra and it’s corollary to find the zeros of a
polynomial?
Assessment: Students will write a summary on ways to use the Fundamental Theorem of Algebra to
find the zeros of a polynomial.
Beginning to find all Zeros
DO NOT WRITE DOWN
Ex. Find all Zeros f (x) = x4 – 8x3 + 18x2 – 27
EQ: How do we use the Fundamental Theorem of Algebra and it’s corollary to find the zeros of a
polynomial?
Assessment: Students will write a summary on ways to use the Fundamental Theorem of Algebra to
find the zeros of a polynomial.
You Try It!
1. How many solutions
does the equation
x4 + 5x2 – 36 = 0 have?
2. How many zeros does
the function
f (x) = x3 + 7x2 + 8x – 16
have?
EQ: How do we use the Fundamental Theorem of Algebra and it’s corollary to find the zeros of a
polynomial?
Assessment: Students will write a summary on ways to use the Fundamental Theorem of Algebra to
find the zeros of a polynomial.
Homework
Textbook - Pg. 383 #3-9