Rogers Bernard
02/14/2023 · Primary School
Suppose that the polynomial function \( f \) is defined as follows. \[ f(x)=(x-11)^{2}(x+4)(x-12)^{2} \] List each zero of \( f \) according to its multiplicity In the categories below. If there is more than one answer for a multiplicty, separate them with commas. If there is no answer, dick on "None." Zero(s) of multiplicity one: Zero(s) of multiplicity two:
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the zeros of the polynomial function \( f(x) = (x-11)^{2}(x+4)(x-12)^{2} \), we need to identify the values of \( x \) that make \( f(x) = 0 \) and their corresponding multiplicities.
1. **Finding the zeros:**
- The factor \( (x-11)^{2} \) gives a zero at \( x = 11 \) with multiplicity 2.
- The factor \( (x+4) \) gives a zero at \( x = -4 \) with multiplicity 1.
- The factor \( (x-12)^{2} \) gives a zero at \( x = 12 \) with multiplicity 2.
2. **Listing the zeros according to their multiplicities:**
- **Zero(s) of multiplicity one:**
- \( -4 \)
- **Zero(s) of multiplicity two:**
- \( 11, 12 \)
Thus, the final answers are:
- Zero(s) of multiplicity one: \( -4 \)
- Zero(s) of multiplicity two: \( 11, 12 \)
Quick Answer
Zero(s) of multiplicity one: -4
Zero(s) of multiplicity two: 11, 12
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit