Analytic Geometry: Trace the curve of x^{3}-6x^{2}+11x-y=6

Douglas Kraatz 2021-11-27 Answered
Analytic Geometry:
Trace the curve of \(\displaystyle{x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{y}={6}\)

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Expert Answer

Linda Tincher
Answered 2021-11-28 Author has 7798 answers
\(\displaystyle{x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{y}={6}\)
\(\displaystyle{y}={x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{6}\)
\(\displaystyle{P}{\left({x}\right)}={x}^{{{3}}}-{6}{x}^{{{2}}}+{11}{x}-{6}\)
\(\displaystyle{P}{\left({z}\right)}={1}-{6}+{11}-{6}={0}\)
(x-l) is a talov of p(x)
Diviwng p(x) by (x-l) we get
\(\displaystyle{2}{\left({x}\right)}={x}^{{{2}}}-{3}{x}-{2}{x}+{6}\)
\(\displaystyle{2}{\left({x}\right)}={x}{\left({x}-{3}\right)}-{2}{\left({x}-{3}\right)}\)
\(\displaystyle{2}{\left({x}\right)}={\left({x}-{2}\right)}{\left({x}-{3}\right)}\)
\(\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{2}{\left({x}\right)}\)
\(\displaystyle{p}{\left({x}\right)}={\left({x}-{1}\right)}{\left({x}-{2}\right)}{\left({x}-{3}\right)}\)
Zowes of polynaval are x=1,2,3
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