Find all the roots (real and imaginary) of the given polynomials. Describe multiplicity when applicable. f(x)=x^4-8x^2-8x+15

CoormaBak9 2021-09-13 Answered
Find all the roots (real and imaginary) of the given polynomials. Describe multiplicity when applicable. Please show all work and simplify your answers.
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{4}}-{8}{x}^{{2}}-{8}{x}+{15}\)

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Expert Answer

sweererlirumeX
Answered 2021-09-14 Author has 22646 answers
Given \(\displaystyle{f{{\left({x}\right)}}}={x}^{{4}}-{8}{x}^{{2}}-{8}{x}+{15}\)
The all the roots of the above expression is
X=1
X=3
X=-2+i
X=-2-i
\(\displaystyle={\left({x}-{1}\right)}{\left({x}-{3}\right)}{\left({x}+{2}-{i}\right)}{\left({x}+{2}+{i}\right)}\)
\(\displaystyle={\left({x}^{{2}}-{3}{x}-{x}+{3}\right)}{\left({x}^{{2}}+{2}{x}+\xi+{2}{x}+{4}+{2}{i}-\xi-{2}{i}+{1}\right)}\)
\(\displaystyle={\left({x}^{{2}}-{4}{x}+{3}\right)}{\left({x}^{{2}}+{4}{x}+{5}\right)}\)
\(\displaystyle={\left({x}^{{4}}+{4}{x}^{{3}}+{5}{x}^{{2}}-{4}{x}^{{3}}-{16}{x}^{{2}}-{20}{x}+{3}{x}^{{2}}+{12}{x}+{15}\right)}\)
\(\displaystyle={x}^{{4}}-{8}{x}^{{2}}-{8}{x}+{15}\)
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