Final answer:
To find the zero(s) at which the polynomial function f(x)=x⁴-5x³-2x²-30x-24 flattens out, we need to find the x-values where the slope of the function is zero. This can be done by finding the derivative of the function and setting it equal to zero. The x-values obtained will be the zero(s) at which the original function f(x) flattens out.
Step-by-step explanation:
To find the zero(s) at which the polynomial function f(x)=x⁴-5x³-2x²-30x-24 flattens out, we need to find the x-values where the slope of the function is zero. This can be done by finding the derivative of the function and setting it equal to zero.
First, we find the derivative of f(x) by taking the derivative of each term: f'(x) = 4x³ - 15x² - 4x - 30. Next, we set the derivative equal to zero and solve for x:
4x³ - 15x² - 4x - 30 = 0
This equation can be solved using factoring, synthetic division, or numerical methods to find the zero(s) of the derivative function. The x-values obtained will be the zero(s) at which the original function f(x) flattens out.
Expressing them as ordered pairs depends on the context or specific requirements of the question.