Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Solve algebraically for all values of xx:
![**Problem Statement:**
Solve algebraically for all values of \( x \):
\[ 5x^4 - 6x^3 = 0 \]
**Solution:**
1. **Factor the equation:**
- Take out the common factor, \( x^3 \):
\[
x^3(5x - 6) = 0
\]
2. **Set each factor to zero and solve:**
- \( x^3 = 0 \):
- Solution: \( x = 0 \)
- \( 5x - 6 = 0 \):
- Solve for \( x \): \( 5x = 6 \)
- \( x = \frac{6}{5} \)
**Conclusion:**
The values of \( x \) that satisfy the equation are:
\[ x = 0 \quad \text{and} \quad x = \frac{6}{5} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F660f3768-04db-40d7-8720-159b99056ea6%2F777d1100-3152-45c2-a88e-f340b5f761e0%2Fe076gwe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve algebraically for all values of \( x \):
\[ 5x^4 - 6x^3 = 0 \]
**Solution:**
1. **Factor the equation:**
- Take out the common factor, \( x^3 \):
\[
x^3(5x - 6) = 0
\]
2. **Set each factor to zero and solve:**
- \( x^3 = 0 \):
- Solution: \( x = 0 \)
- \( 5x - 6 = 0 \):
- Solve for \( x \): \( 5x = 6 \)
- \( x = \frac{6}{5} \)
**Conclusion:**
The values of \( x \) that satisfy the equation are:
\[ x = 0 \quad \text{and} \quad x = \frac{6}{5} \]
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