To find the zeros of the polynomial function [tex]\( f(x) = x^4 - 7x^3 - 39x^2 - 53x - 22 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 0 \)[/tex]. Here is a step-by-step solution:
1. Polynomial [tex]\( f(x) \)[/tex]:
[tex]\[ f(x) = x^4 - 7x^3 - 39x^2 - 53x - 22 \][/tex]
2. Formulate the equation:
We solve for [tex]\( x \)[/tex] in the equation:
[tex]\[ x^4 - 7x^3 - 39x^2 - 53x - 22 = 0 \][/tex]
3. Solve the polynomial equation:
Solving this polynomial equation yields the zeros of the function.
4. List the zeros from smallest to largest:
After solving, we find the zeros to be [tex]\( -2 \)[/tex], [tex]\( -1 \)[/tex], and [tex]\( 11 \)[/tex].
5. Arrange the zeros:
Since we list the zeros from smallest to largest, we put them in the order:
[tex]\[ x = [-2, -1, 11] \][/tex]
Therefore, the zeros of the polynomial [tex]\( f(x) = x^4 - 7x^3 - 39x^2 - 53x - 22 \)[/tex] arranged from smallest to largest are:
[tex]\[ x = [-2, -1, 11] \][/tex]
