Find roots of polynomial $$ p(x) = -\frac{3}{8}x^4-x^3+2x^2+5 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.934\\[1 em]x_2 &= -4.142\\[1 em]x_3 &= -0.2294+1.2696i\\[1 em]x_4 &= -0.2294-1.2696i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 8 } $.
$$ \begin{aligned} -\frac{3}{8}x^4-x^3+2x^2+5 & = 0 ~~~ / \cdot \color{blue}{ 8 } \\[1 em] -3x^4-8x^3+16x^2+40 & = 0 \end{aligned} $$Step 2:
Polynomial $ -3x^4-8x^3+16x^2+40 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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