Answered

Get expert advice and insights on any topic with IDNLearn.com. Our platform provides accurate, detailed responses to help you navigate any topic with ease.

Find the zeros of the function and state the multiplicities.

[tex]\[ g(x) = -3x^4(x + 2)^3(x + 4)^2 \][/tex]

If there is more than one answer, separate them with commas. Select "None" if applicable.

Part 1 of 2

The zero(s) of [tex]\( g \)[/tex]:
[tex]\[
\begin{array}{|c|c|}
\hline
\square & \text{Multiplicity: } \square \\
\hline
\square & \text{Multiplicity: } \square \\
\hline
\square & \text{Multiplicity: } \square \\
\hline
\square & \text{Multiplicity: } \square \\
\hline
\end{array}
\][/tex]

None [tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
To find the zeros of the function [tex]\( g(x) = -3x^4(x+2)^3(x+4)^2 \)[/tex], we need to set [tex]\( g(x) = 0 \)[/tex] and solve for [tex]\( x \)[/tex].

### Step-by-step Solution:

1. Identify the factors of the function:
The function [tex]\( g(x) \)[/tex] is given as:
[tex]\[ g(x) = -3x^4(x+2)^3(x+4)^2 \][/tex]
Each factor must be set to zero and solved for [tex]\( x \)[/tex].

2. Set each factor to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ x^4 = 0 \][/tex]
Solving for [tex]\( x \)[/tex] gives:
[tex]\[ x = 0 \][/tex]
[tex]\[ (x+2)^3 = 0 \][/tex]
Solving for [tex]\( x \)[/tex] gives:
[tex]\[ x = -2 \][/tex]
[tex]\[ (x+4)^2 = 0 \][/tex]
Solving for [tex]\( x \)[/tex] gives:
[tex]\[ x = -4 \][/tex]

3. List the zeros:
The zeros of the function [tex]\( g(x) \)[/tex] are:
[tex]\[ 0, -2, -4 \][/tex]

### Answer for Part 1:
The zero(s) of [tex]\( g \)[/tex]:
[tex]\[ 0, -2, -4 \][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and see you next time for more reliable information.