Question

Find all the rational zeros for the following function f(x)=x³ 12-13x -4?

1) 1, 3
2) -4, -3
3) 1, 3, -4
4) -2, 3, -4

Answer 1

The rational zeros of the function f(x) = x³ - 13x² + 12x - 4 are 1 and -4.

Step-by-step explanation:

To find the rational zeros of the function f(x) = x³ - 13x² + 12x - 4, we can apply the Rational Root Theorem. The Rational Root Theorem states that if a rational number p/q is a zero of the polynomial, then p must be a factor of the constant term (in this case, 4), and q must be a factor of the leading coefficient (in this case, 1).

By testing the factors of 4 (1, 2, 4) and 1 (1), we can determine the possible rational zeros.

After testing these possible zeros by synthetic division, we find that the rational zeros of the function are 1 and -4. Therefore, the correct answer is option 3) 1, 3, -4.