Math Problem Statement
Find all values of x for which g(x)=0
Find all values of x for which g(x) = 0.
Solution
To solve for all values of where , we start by analyzing the function , which is given as:
The function equals zero when any of the factors in the product equals zero. Therefore, we need to solve the following equations:
Solving each equation:
Solution:
The values of that satisfy are:
Would you like more details or have any questions? Here are some related questions:
- What are the roots of the function for the given ?
- How do the graphs of and compare?
- Can have any maximum or minimum points? How would you find them?
- What is the multiplicity of each root of ?
- How does factoring help in solving polynomial equations?
Tip: When solving polynomial equations, always check the factors individually to determine the roots of the equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Equations
Factoring
Formulas
g(x) = (2x + 3)(x + 2)(x - 1)
Theorems
Zero Product Property
Suitable Grade Level
Grades 9-12