Find the roots of the function g(x)=x^3 +16x
a)0,4i, -4i
b)0,-4,-4i
c)0,4,4i
d)0,4,-4
The equation can be rewritten
x(x^2 + 16) = 0
The function is zero if x = 0, OR if
x^2 = -16
That should give you a hint of what the roots are.
So you take the square root of -16 which gives you +- 4 making the answer d. Right?
No. The square root of -16 is 4i and -41.
i = sqrt (-1)
The answer is (a). I mistakenly typed
-41 for -4i
To find the roots of the function g(x) = x^3 + 16x, we need to solve the equation g(x) = 0. Let's break it down step by step:
1. Start with the original function: g(x) = x^3 + 16x.
2. Set g(x) equal to zero: x^3 + 16x = 0.
3. Factor out an x from this equation: x(x^2 + 16) = 0.
4. Now we have two possibilities: either x = 0 or x^2 + 16 = 0.
5. For x = 0, we have found one root of the equation.
6. For x^2 + 16 = 0, we need to solve this equation for x by subtracting 16 from both sides: x^2 = -16.
7. Take the square root of both sides: x = ±√(-16).
8. Remember that the square root of -1 is denoted as "i" (i.e., i = √(-1)). So, √(-16) can be written as ±4i.
9. Therefore, the roots of the equation x^2 + 16 = 0 are x = 4i and x = -4i.
10. Combining the root x = 0 with the roots x = 4i and x = -4i, we get the answer: the roots of the function g(x) = x^3 + 16x are 0, 4i, and -4i.
11. So, the correct answer is (a) 0, 4i, -4i.