Question

f(x) = x.3 + 4x.2 + x – 6 Determine the number of real zeros

Answer 1

Since a + b + c + d = 0, one real root of the equation f(x) = 0 is 1. One factor of f(x) is (x - 1). Divide f(x) by (x - 1) ->
f(x) = (x - 1)(x^2 + 5x + 6). This trinomial can be factored into: (x + 3)(x + 2)
Finally, f(x) = (x -1)(x +2)(x + 3). The roots zeros are: 1, -2, and -3.