Question

Find the zeros of the function f(x) = x³ - 5x² + 6x using a calculator:

A) x = 0, x = 3
B) x = 1, x = 2
C) x = -1, x = 6
D) x = -2, x = 3

Answer 1

The zeros of the function f(x) = x³ - 5x² + 6x are obtained by factoring and are x = 0, x = 2, and x = 3. There seems to be a typo in the provided options as they do not include this set of zeros.

Step-by-step explanation:

To find the zeros of the function f(x) = x³ - 5x² + 6x, we can factor the polynomial. First, note that there is a common factor of x, which gives us:

x(x² - 5x + 6) = 0

Now we can factor the quadratic part:

x(x - 2)(x - 3) = 0

The zeros of the function are the values of x that make the equation equal to zero. Therefore, the zeros are x = 0, x = 2, and x = 3. Since the solution is not listed as an option in the multiple choice, there might be a typo in the options given.