Solve the equation
x3 - 4x2 + 16x - 64 = 0 by finding all the roots if 4
is one of the roots.

3 roots are:

4, 4i, -4i

Step-by-step explanation:

This is a cubic equation that has 3 roots. One root is given, we got to find the other two.

Let's group first 2 terms and last two terms and factor and solve:

From here we can say:

x^2 + 16 = 0

and

x - 4 = 0 [x = 4, we already know this solution]

Let's find the other 2 roots from the 1st equation:

Note:

So the 3 roots are:

4, 4i, -4i