1. Find the roots (zeros) for P(x) = x4 - 6x³ + 9x² + 4x - 12. For this process exam, you DO NOT need to detail your steps. You simply need to show your work and state the answers to the specified topics. a. State how to find all possible zeros AND list all possible zeros b. State how to find how many possible POSITIVE roots exist AND list how many possible POSITIVE roots exist c. State how to find how many possible NEGATIVE roots exist AND list how many possible NEGATIVE roots exist d. Use synthetic division or long division to find the actual roots e. Write P(x) in factored form
1. Find the roots (zeros) for P(x) = x4 - 6x³ + 9x² + 4x - 12. For this process exam, you DO NOT need to detail your steps. You simply need to show your work and state the answers to the specified topics. a. State how to find all possible zeros AND list all possible zeros b. State how to find how many possible POSITIVE roots exist AND list how many possible POSITIVE roots exist c. State how to find how many possible NEGATIVE roots exist AND list how many possible NEGATIVE roots exist d. Use synthetic division or long division to find the actual roots e. Write P(x) in factored form
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Exercise: Finding the Roots (Zeros)**
Consider the polynomial \( P(x) = x^4 - 6x^3 + 9x^2 + 4x - 12 \).
For this exercise, detailing your steps is not required. Simply show your work and state the answers to the specified topics below:
a. **Finding All Possible Zeros**
- State the method to find all possible zeros and list them.
b. **Positive Roots**
- Explain how to determine the number of possible positive roots and provide a list of how many possible positive roots exist.
c. **Negative Roots**
- Explain how to determine the number of possible negative roots and provide a list of how many possible negative roots exist.
d. **Using Synthetic or Long Division**
- Use synthetic division or long division to find the actual roots of the polynomial.
e. **Factored Form**
- Write \( P(x) \) in its factored form.
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