(a) Determine the possible numbers of positive and negative real zeros of f and (b) list the possible rational zeros of f.

Question

f(x) = x^3 +x^2 - 4x - 4

Answer 1

p = +or-{1,2,4}; q= +or- 1

p/q = p = +or- {1,2,4}

f(-1) = -1 + 1 + 4 - 4 = 0

-1 | 1 1 -4 -4

-1 0 4

_________________

1 0 -4 0

so x=-1 is a solution and then remaining polynomial is x^2-4 = (x+2)(x-2)

the complete solution set is x={-1,2,-2}; note that x=-2,2 are in the list!