What are the zeros of the function $f(x)=x^{2}+2 x-24$ ?
-8 and 3
-6 and 4
-4 and 6
-3 and 8
-2 and 24

Step 1 ：The zeros of a function are the x-values for which the function equals zero. In other words, they are the solutions to the equation \(f(x) = 0\). In this case, we need to solve the equation \(x^{2}+2 x-24 = 0\). This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. The quadratic formula seems to be the most straightforward method in this case.

Step 2 ：Given the quadratic equation \(ax^{2} + bx + c = 0\), the solutions can be found using the quadratic formula \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\).

Step 3 ：For the given function \(f(x)=x^{2}+2 x-24\), the coefficients are: \(a = 1\), \(b = 2\), and \(c = -24\).

Step 4 ：Calculate the discriminant \(D = b^{2} - 4ac = 100\).

Step 5 ：Substitute the coefficients and the discriminant into the quadratic formula to find the solutions: \(x1 = -6.0\) and \(x2 = 4.0\).

Step 6 ：Final Answer: The zeros of the function \(f(x)=x^{2}+2 x-24\) are \(\boxed{-6}\) and \(\boxed{4}\).