Question

If f(x) = x^3 - 6x^2 - 25x - 18 ) and f(-1) = 0 , find all the zeros of f(x) algebraically.

a) ( x = -3, 2 )
b) ( x = -1, 3 )
c) ( x = -2, 9 )
d) ( x = 1, -6 )

Answer 1

To find the zeros of the function f(x) = x^3 - 6x^2 - 25x - 18, we can set f(x) equal to zero and solve for x. The zeros are x = -1 and x = 3.

Step-by-step explanation:

To find the zeros of the function f(x) = x^3 - 6x^2 - 25x - 18, we can set f(x) equal to zero and solve for x.

Since f(-1) = 0, we know that x = -1 is one of the zeros.

To find the other zeros, we need to factor the polynomial. By using long division or synthetic division, we can divide f(x) by (x + 1) and obtain a quadratic factor of f(x).

By solving the quadratic equation, we can find the value of x that satisfies f(x) = 0, which will give us the other zero. The correct answer is option b) (x = -1, 3).