Question

Find the zeros of f(x)=2x^4-5x^3+11x^2-35x-21

Answer 1

2x^4-5x^3+11x^2-35x-21

factor by grouping.
(2x^4-5x^3)(11x^2-35x) - 21
x^3(2x-1) x(11x-35) - 21
(x^3+x- 21)(11x-35)(2x-1)

factor again by grouping
(x^3+x- 21)
x(x^2+1)-21
x = 21
x^2 = -1
after squarerooting both sides you're left with imaginary numbers as well:
x=+-1i

(11x-35)
11x=35
x = (35/11)

(2x-1)
2x=1
x=(1/2)

so your zeros are:

x=(1/2)
x = (35/11)
x=-1i
x=+1i
x = 21