I need some help with my math homework!!

Question

X^8-28x^5+27x^2=0

Answer 1

x⁸ - 28x⁵ + 27x² = 0

 

x²(x⁶ - 28x³ + 27) = 0

 

x²(x³ - 1)(x³ - 27) = 0

 

x²(x - 1)(x² + x + 1)(x - 3)(x² + 3x + 9) = 0

 

So setting each factor to 0 and solving gives all roots, real and complex.

 

Real: x = 0 (multiplicity 2), x = 1, x = 3

 

Complex conjugate pairs:

 

x = (-1 ± i√3)/2

 

x = (-3 ± 3i√3)/2

Answer 2

x=1,0, or 3