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