Question

what are the zeros to the function? f(x) = 3x² + 75 *type the numbers separated by a comma. no spaces. enter answer here

Explanation:

Step1: Set function to zero

To find the zeros of the function \( f(x) = 3x^2 + 75 \), we set \( f(x) = 0 \). So we have the equation:
\[
3x^2 + 75 = 0
\]

Step2: Simplify the equation

First, we can divide the entire equation by 3 to simplify it. Dividing each term by 3 gives:
\[
x^2 + 25 = 0
\]
Then, we can rewrite this as:
\[
x^2 = -25
\]

Step3: Solve for \( x \)

To solve for \( x \), we take the square root of both sides. Remember that the square root of a negative number involves the imaginary unit \( i \), where \( i^2 = -1 \). So:
\[
x = \pm\sqrt{-25} = \pm\sqrt{25 \times (-1)} = \pm(5i)
\]
So the zeros of the function are \( 5i, -5i \).

Answer:

5i,-5i