What are the roots of g(x)=4x^2+256 ? Provide the exact answers. Enter the smaller number first.(1 point)

Answer 1

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

4x^2 + 256 = 0

Let's first subtract 256 from both sides:

4x^2 = -256

Now, divide both sides by 4:

x^2 = -64

Now, take the square root of both sides:

x = ±√(-64)

Since taking the square root of a negative number involves complex numbers, we can write the square root of -64 as:

x = ±8i

So, the roots of g(x) = 4x^2 + 256 are x = 8i and x = -8i.