# One of the zeros is given for each of the following polynomials. Find the other zeros in the field of complex numbers.x^3-4x^2+6x-4.1-i is a zero

One of the zeros is given for each of the following polynomials. Find the other zeros in the field of complex numbers.
$$\displaystyle{x}^{{3}}-{4}{x}^{{2}}+{6}{x}-{4.1}-{i}$$ is a zero

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diskusje5

We have given one roots of the polynomial $$\displaystyle{x}^{{3}}-{4}{x}^{{2}}+{6}{x}-{4}$$ is 1-i then other root will be 1+i since, roots of polynomial occur in complex conjugate.
Now, we have to find just one real roots.
For check x=2 we see
$$\displaystyle{x}^{{3}}-{4}{x}^{{2}}+{6}{x}={\left({2}\right)}^{{3}}-{4}{\left({2}\right)}^{{2}}+{6}{\left({2}\right)}-{4}$$
$$\displaystyle={8}-{16}+{12}-{4}$$
$$\displaystyle={0}$$
Therefore, x=2 is a real root of the function.
Therefore, another two roots of the polynomials are 2,1+i