Find all of the zeros of the function f(x) = x^4 - 3x^3 + 2x - 4

Question

Please answer this question and show me how you got it.

Answer 1

x f(x)

0 -4

1 --4

2 -8

3 2 one zero is between 2 and 3 as f(x) changes sign, the zero is closer to 3 than to 2

-1 -2

-2 32 another zero is between -1 and -2 as f(x) changes sign, the zero is closer to -1 than to -2

there might be another zero or two between 0 and 1. the graph is "W" shaped. The middle of the "W" is a local maximum, but f(1/2) =- 3 1/4, so there doesn't appear to be any real zero between 0 and 1

there are potentially 4 real zeroes with a 4th degree polynomial

there are potentially 3 positive real zeros, by Descartes' rule of signs

there is only 1 negative real zero