x⁴-5x³+5x²-5x+4.
By observation x=1 is a zero because:
1-5+5-5+4=0.
Divide by the root:
1 | 1 -5 5 -5 | 4
1 1 -4 1 | -4
1 -4 1 -4 | 0
Cubic is x³-4x²+x-4=x²(x-4)+(x-4)=(x²+1)(x-4).
So factorisation is (x-1)(x-4)(x²+1).
Zeroes are 1, 4, i, -i, where i=√-1, an imaginary number.