Find the number of solutions or zeros

1

EXAMPLE 1
Find the number of solutions or zeros
a. How many solutions does the equation
x3 5x2 4x 20 0 have?
SOLUTION
Because x3 5x2 4x 20 0 is a polynomial
equation of degree 3,it has three solutions.
(The solutions are 5, 2i, and 2i.)
2

EXAMPLE 1
Find the number of solutions or zeros
b. How many zeros does the function f
(x) x4 8x3 18x2 27 have?
SOLUTION
Because f (x) x4 8x3 18x2 27 is a
polynomial function of degree 4, it has four
zeros. (The zeros are 1, 3, 3, and 3.)
3
for Example 1
GUIDED PRACTICE
1. How many solutions does the equation
x4 5x2 36 0 have?
4
for Example 1
GUIDED PRACTICE
2. How many zeros does the function f
(x) x3 7x2 8x 16 have?