Answer :
To find the zeros of the function [tex]\( s(x) = x^4 - 9x^2 + 3x^3 - 27x - 10x^2 + 90 \)[/tex], we first simplify the expression by combining like terms.
1. Simplify the expression:
Let's combine like terms in the polynomial:
[tex]\[
s(x) = x^4 + 3x^3 - 9x^2 - 10x^2 - 27x + 90
\][/tex]
Combining the [tex]\( x^2 \)[/tex] terms, we have:
[tex]\[
s(x) = x^4 + 3x^3 - 19x^2 - 27x + 90
\][/tex]
2. Find the zeros of the simplified polynomial:
To determine the zeros of the polynomial [tex]\( s(x) = x^4 + 3x^3 - 19x^2 - 27x + 90 \)[/tex], we need to solve the equation [tex]\( s(x) = 0 \)[/tex].
The zeros of this polynomial are
[tex]\[
x = -5, -3, 2, \text{ and } 3
\][/tex]
These values of [tex]\( x \)[/tex] are the solutions where the polynomial equals zero. Therefore, these are the zeros of the given function.
1. Simplify the expression:
Let's combine like terms in the polynomial:
[tex]\[
s(x) = x^4 + 3x^3 - 9x^2 - 10x^2 - 27x + 90
\][/tex]
Combining the [tex]\( x^2 \)[/tex] terms, we have:
[tex]\[
s(x) = x^4 + 3x^3 - 19x^2 - 27x + 90
\][/tex]
2. Find the zeros of the simplified polynomial:
To determine the zeros of the polynomial [tex]\( s(x) = x^4 + 3x^3 - 19x^2 - 27x + 90 \)[/tex], we need to solve the equation [tex]\( s(x) = 0 \)[/tex].
The zeros of this polynomial are
[tex]\[
x = -5, -3, 2, \text{ and } 3
\][/tex]
These values of [tex]\( x \)[/tex] are the solutions where the polynomial equals zero. Therefore, these are the zeros of the given function.
