Solve the polynomial inequality graphically. 2x^{3}-5x^{2}-x+6>0

Solve the polynomial inequality graphically. 2x^{3}-5x^{2}-x+6>0

Question
Polynomial graphs
asked 2020-10-27
Solve the polynomial inequality graphically. \(\displaystyle{2}{x}^{{{3}}}-{5}{x}^{{{2}}}-{x}+{6}{>}{0}\)

Answers (1)

2020-10-28
Step 1 image Step 2 \(\displaystyle{2}{x}^{{{3}}}-{5}{x}^{{{2}}}-{x}+{6}{>}{0}\) To solve graphically we graph \(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}-{5}{x}^{{{2}}}-{x}+{6}\). A 3rd degree polinomial can have up to 3 zeros, so make sure you can see all the important parts of the graph. We find zeros at: \(\displaystyle{x}=-{1},{1.5},{2}\) For the inequality, they want \(\displaystyle{f{{\left({x}\right)}}}{>}{0}\), which are the parts of the graph above the x-axis. We can see from the graph they are the intervals. Answer: \(\displaystyle{\left(-{1},{1.5}\right)}\cup{\left({2},\infty\right)}\)
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