For the given polynomial o find the maximum possible numbers of the positive and the negative root. o find all the integer roots o find the non-integer real roots o find the complex roots d(x)=x°-64 the maximum possible number of positive roots is the maximum possible number of negative roots the integer root (s) is are Example: x-3; x=5 the non- integer real (s) roots is are Example:x=3: x-5 the complex root (s) is are Evample: x-3: -5

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Polynomial Root Analysis**

**For the given polynomial:**
- Find the maximum possible number of positive and negative roots.
- Find all the integer roots.
- Find the non-integer real roots.
- Find the complex roots.

Given Polynomial:

\[d(x) = x^6 - 64\]

**Tasks:**

1. **Maximum possible number of positive roots:** [ ]
2. **Maximum possible number of negative roots:** [ ]
3. **Integer roots (if any):** Example: \(x = 3, x = -5\)
4. **Non-integer real roots (if any):** Example: \(x = 3, x = -5\)
5. **Complex roots (if any):** Example: \(x = 3, x = -5\)

Use various methods such as Descartes' Rule of Signs, polynomial factorization, and the quadratic formula to determine the roots.
Transcribed Image Text:**Polynomial Root Analysis** **For the given polynomial:** - Find the maximum possible number of positive and negative roots. - Find all the integer roots. - Find the non-integer real roots. - Find the complex roots. Given Polynomial: \[d(x) = x^6 - 64\] **Tasks:** 1. **Maximum possible number of positive roots:** [ ] 2. **Maximum possible number of negative roots:** [ ] 3. **Integer roots (if any):** Example: \(x = 3, x = -5\) 4. **Non-integer real roots (if any):** Example: \(x = 3, x = -5\) 5. **Complex roots (if any):** Example: \(x = 3, x = -5\) Use various methods such as Descartes' Rule of Signs, polynomial factorization, and the quadratic formula to determine the roots.
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