Answer:
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:
[tex]x^3 - 4x^2 + 16x - 64 = 0\\x^2(x-4) + 16(x-4)=0\\(x^2+16)(x-4)=0[/tex]
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:
[tex]x^2 + 16 = 0\\x^2=-16\\x=+-4i[/tex]
Note: [tex]\sqrt{-1}=i[/tex]
So the 3 roots are:
4, 4i, -4i
