Problem

Given the function \(f(x) = x^3 - 3x^2 - 4x + 12\), find the zeros of the function and their multiplicities.

Answer

Expert–verified
Hide Steps
Answer

Finally, set each factor equal to zero to find the zeros: \(x-3 = 0\), \(x-2 = 0\), and \(x+2 = 0\). The solutions are \(x = 3\), \(x = 2\), and \(x = -2\).

Steps

Step 1 ：First, we set the function equal to zero to solve for x: \(x^3 - 3x^2 - 4x + 12 = 0\).

Step 2 ：Next, we attempt to factor the function: \(f(x) = x^3 - 3x^2 - 4x + 12 = (x-3)(x-2)(x+2)\).

Step 3 ：Finally, set each factor equal to zero to find the zeros: \(x-3 = 0\), \(x-2 = 0\), and \(x+2 = 0\). The solutions are \(x = 3\), \(x = 2\), and \(x = -2\).

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More