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 xx where g(x)=0g(x) = 0, we start by analyzing the function g(x)g(x), which is given as:

g(x)=(2x+3)(x+2)(x1)g(x) = (2x + 3)(x + 2)(x - 1)

The function g(x)g(x) equals zero when any of the factors in the product equals zero. Therefore, we need to solve the following equations:

  1. 2x+3=02x + 3 = 0
  2. x+2=0x + 2 = 0
  3. x1=0x - 1 = 0

Solving each equation:

  1. 2x+3=02x + 3 = 0

2x=32x = -3 x=32x = -\frac{3}{2}

  1. x+2=0x + 2 = 0

x=2x = -2

  1. x1=0x - 1 = 0

x=1x = 1

Solution:

The values of xx that satisfy g(x)=0g(x) = 0 are:

x=32,2,1x = -\frac{3}{2}, -2, 1

Would you like more details or have any questions? Here are some related questions:

  1. What are the roots of the function h(x)=0h(x) = 0 for the given h(x)h(x)?
  2. How do the graphs of g(x)g(x) and h(x)h(x) compare?
  3. Can g(x)g(x) have any maximum or minimum points? How would you find them?
  4. What is the multiplicity of each root of g(x)g(x)?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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