What are the roots of g(x)=4x^2+256 ? Provide the exact answers. Enter the smaller number first.

Answer 1

To find the roots of the quadratic equation \( g(x) = 4x^2 + 256 \), we can set the equation equal to zero and solve for \( x \):

\[ 4x^2 + 256 = 0 \]

First, we can isolate the \( x^2 \) term:

\[ 4x^2 = -256 \]

Now, divide both sides by 4:

\[ x^2 = -64 \]

Next, take the square root of both sides. Since we have a negative number under the square root, we will get complex roots:

\[ x = \pm \sqrt{-64} \]

This can be simplified as:

\[ x = \pm 8i \]

Therefore, the roots of the equation \( g(x) = 4x^2 + 256 \) are:

\[ -8i \quad \text{and} \quad 8i \]

In exact form, the smaller number first is:

\[ -8i, \quad 8i \]