To find the zeros of the function f(x) = x^3 - 6x^2 + 3x + 10, we need to find the values of x where the function equals zero.
To do this, we can use various methods such as factoring, the rational root theorem, or graphing the function. In this case, let's use factoring.
1. Start by setting the function equal to zero:
x^3 - 6x^2 + 3x + 10 = 0
2. Try to factor the equation by grouping terms. In this case, factoring may not be straightforward. We can try different factorizations or use alternative methods.
3. If factoring is not immediately apparent, we can use numerical methods or graphing software to approximate the zeros. Using a graphing calculator or software, we can plot the function and identify the x-intercepts, where the graph crosses the x-axis.
4. Based on graphing the function, we find that it has one real zero, approximately x ≈ 3.718. This means that the function intersects the x-axis at x ≈ 3.718.
Therefore, the zero of the function f(x) = x^3 - 6x^2 + 3x + 10 is approximately x ≈ 3.718.