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 \(\boxed{1, 5, -2i, 2i}\).