Find roots of polynomial $$ p(x) = -8x^4+\frac{73}{9}x^2+4 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1735\\[1 em]x_2 &= -1.1735\\[1 em]x_3 &= 0.6026i\\[1 em]x_4 &= -0.6026i \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 9 } $.
$$ \begin{aligned} -8x^4+\frac{73}{9}x^2+4 & = 0 ~~~ / \cdot \color{blue}{ 9 } \\[1 em] -72x^4+73x^2+36 & = 0 \end{aligned} $$Step 2:
Polynomial $ -72x^4+73x^2+36 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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