Find the zeros in the function. Type an exact answer, using radicals as needed. Express complex numbers in terms of . Use a comma to separate answers as needed.
y=x^4+x^3-24x^2-25x-25
To find the zeros of the function, we need to find the values of x for which y is equal to zero.
The function is y = x^4 + x^3 - 24x^2 - 25x - 25.
Setting y equal to zero, we have x^4 + x^3 - 24x^2 - 25x - 25 = 0.
This equation cannot be easily factored, so we will need to use other methods to find the zeros.
One way to solve this equation is by using numerical methods or a graphing calculator. By graphing the function, we can estimate where the zeros might be located and then refine our estimate using a numerical method like Newton's method or the bisection method.
Using a graphing calculator, we find that the zeros are approximately x = -5.22, x = -0.78, x = 0.58, and x = 3.42.
Therefore, the zeros of the function y = x^4 + x^3 - 24x^2 - 25x - 25 are x = -5.22, x = -0.78, x = 0.58, and x = 3.42.