Question

How many roots (real and complex) describe the given polynomial function?

Answer 1

one way is try to find the roots.

Answer 2

@TurtleMuffin

Answer 3

Let's factor f(x).

f(x) = x^3 + 16x = x(x^2 + 16).

If f(x) = 0, then 0 = x(x^2+16).

This means either x=0 or (x^2+16).

x=0 is one root. However, x^2+16 is just like that parabola I described in the last problem! It never touches the x-axis, since the +16 shifts it upwards.

So, that has two imaginary roots. Therefore, f(x) has two imaginary roots.

Answer 4

so two real roots one complex root?