Question

6 of 10
what are the zeros to the function?
f(x) = 4x³ + 144x
*type the numbers separated by a comma. no spaces.
enter answer here

Explanation:

Step1: Factor out the GCF

First, factor out the greatest common factor (GCF) from the function \( f(x) = 4x^3 + 144x \). The GCF of \( 4x^3 \) and \( 144x \) is \( 4x \). So we have:
\( f(x) = 4x(x^2 + 36) \)

Step2: Set each factor equal to zero

To find the zeros, we set \( f(x) = 0 \), which gives us two equations:

1. \( 4x = 0 \)
2. \( x^2 + 36 = 0 \)

For the first equation \( 4x = 0 \), dividing both sides by 4 gives \( x = 0 \).

For the second equation \( x^2 + 36 = 0 \), we can rewrite it as \( x^2 = -36 \). Taking the square root of both sides, we get \( x = \pm\sqrt{-36} \). Since \( \sqrt{-36} = 6i \) (where \( i \) is the imaginary unit, \( i^2 = -1 \)), the solutions for this equation are \( x = 6i \) and \( x = -6i \).

Answer:

0,6i,-6i