find all roots y=2x^4-2x^3-2x^2-2x-4

Question

trying to find the roots please help

Answer 1

2x⁴-2x³-2x²-2x-4=2(x⁴-x³-x²-x-2).

By inspection, x=-1 is a zero: 2(1+1-1+1-2)=0.

Divide by this zero:

-1 | 1 -1 -1 -1  -2

      1 -1  2 -1 | 2

      1 -2  1 -2 | 0 = x³-2x²+x-2=x(x²+1)-2(x²+1)=(x-2)(x²+1).

So the remaining zeroes are 2, i, -i.

Zeroes are -1, 2, i, -i.