estion 9 of 9 , Step 1 of 1
$10 / 15$
Correct
d all zeros of the following polynomial. Be sure to find the appropriate number of solutions (counting multiplicity) using the Linear Factors The
\[
f(x)=x^{5}-11 x^{4}+39 x^{3}-69 x^{2}+140 x-100
\]
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Step 1 ：The question is asking to find all zeros of the given polynomial. The zeros of a polynomial are the values of x for which the polynomial equals zero. To find the zeros of the polynomial, we can set the polynomial equal to zero and solve for x.

Step 2 ：The given polynomial is \(f(x)=x^{5}-11 x^{4}+39 x^{3}-69 x^{2}+140 x-100\).

Step 3 ：Setting the polynomial equal to zero gives us \(x^{5}-11 x^{4}+39 x^{3}-69 x^{2}+140 x-100 = 0\).

Step 4 ：Solving this equation gives us the zeros of the polynomial, which are \(x = 1, 5, -2i, 2i\).

Step 5 ：Final Answer: The zeros of the polynomial are \(\boxed{1, 5, -2i, 2i}\).