About Finding the Zeros of a Polynomial Function:
When we are asked to find the zeros of a polynomial function, we are trying to find the x-value or x-values for which the function is equal to zero.
Test Objectives
- Demonstrate the ability to find the zeros for a polynomial function
#1:
Instructions: Find all zeros.
a) f(x) = x3 + 5x2 + 8x - 96
b) f(x) = x3 - x2 - 53x + 165
Watch the Step by Step Video Lesson View the Written Solution
#2:
Instructions: Find all zeros.
a) f(x) = x3 - 2x2 - 16x + 32
b) f(x) = x4 - 5x3 + 11x2 - 15x
Watch the Step by Step Video Lesson View the Written Solution
#3:
Instructions: Find all zeros.
a) f(x) = x5 + 2x4 - 18x3 - 36x2 + 81x + 162
b) f(x) = x4 + 16x3 + 54x2 - 16x - 55
Watch the Step by Step Video Lesson View the Written Solution
#4:
Instructions: Find all zeros.
a) f(x) = x4 + 5x3 - 8x - 40
b) f(x) = x4 + 6x3 + 6x2 - 12x - 16
Watch the Step by Step Video Lesson View the Written Solution
#5:
Instructions: Find all zeros.
a) f(x) = x4 + 8x3 + 11x2 - 32x - 60
b) f(x) = x5 + x4 - 5x3 + 5x2 + 4x - 6
Watch the Step by Step Video Lesson View the Written Solution
Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}-4 \pm 4i, 3$$
$$b)\hspace{.2em}-2 \pm \sqrt{37}, 5$$
Watch the Step by Step Video Lesson
#2:
Solutions:
$$a)\hspace{.2em}\pm 4, 2$$
$$b)\hspace{.2em}0, 3, 1 \pm 2i$$
Watch the Step by Step Video Lesson
#3:
Solutions:
$$a)\hspace{.2em}-2, 3 \hspace{.1em}\text{mult.}\hspace{.1em}2, -3 \hspace{.1em}\text{mult.}\hspace{.1em}2$$
$$b)\hspace{.2em}\pm 1, -11, -5$$
Watch the Step by Step Video Lesson
#4:
Solutions:
$$a)\hspace{.2em}-5, 2, -1 \pm i \sqrt{3}$$
$$b)\hspace{.2em}-4, -2, \pm \sqrt{2}$$
Watch the Step by Step Video Lesson
#5:
Solutions:
$$a)\hspace{.2em}-5, -3, \pm 2$$
$$b)\hspace{.2em}\pm 1, -3, 1 \pm i$$
