Solve the equation x^3 – 5x^2 + 2x + 8

Elleanor Mckenzie 2021-08-16 Answered
Solve the equation \(\displaystyle{x}^{{3}}–{5}{x}^{{2}}+{2}{x}+{8}={0}\) given that -1 is a zero of \(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}–{5}{x}^{{2}}+{2}{x}+{8}\)

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Expert Answer

SchulzD
Answered 2021-08-17 Author has 18295 answers
Divide f(x) by (x +1)
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{3}}–{5}{x}^{{2}}+{2}{x}+{8}={\left({x}+{1}\right)}{\left({x}^{{2}}–{6}{x}+{8}\right)}\)
f(x) = 0, then
\(\displaystyle{x}^{{2}}–{6}{x}+{8}={0}\)
\(\displaystyle{\left({x}–{4}\right)}{\left({x}–{2}\right)}={0}\)
x = 2. 4
The solution is \(\displaystyle{\left\lbrace-{1}.{2}.{4}\right\rbrace}\)
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