Question: determine the number of real zeros of the function f(x) = x.3 + 4x.2 + x – 6.
f(x) = x^3 + 4x^2 + x – 6.
"i keep getting hte answer 1,-2, -3 but when i type it in it always says its wrong."
You are correct!
If x = a is a zero of a function, then (x+a) is a factor of that function.
The factors of your function are: (x - 1), (x + 2), (x + 3).
The function will be a product of those factors (to a constant multiple)
i.e. f(x) = K*(x - 1)(x + 2)(x + 3).
f(x) = K*(x - 1)(x^2 + 5x + 6)
f(x) = K*(x^3 + 5x^2 + 6x - x^2 - 5x - 6)
f(x) = K*(x^3 + 4x^2 + x - 6)
Putting K = 1, we get the orginal function, thus verifying your solution.