Find roots of polynomial $$ p(x) = \frac{35}{8}x^4-\frac{15}{4}x^2+\frac{3}{8} $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.34\\[1 em]x_2 &= 0.34\\[1 em]x_3 &= 0.8611\\[1 em]x_4 &= -0.8611 \end{aligned} $$Explanation
Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 8 } $.
$$ \begin{aligned} \frac{35}{8}x^4-\frac{15}{4}x^2+\frac{3}{8} & = 0 ~~~ / \cdot \color{blue}{ 8 } \\[1 em] 35x^4-30x^2+3 & = 0 \end{aligned} $$Step 2:
Polynomial $ 35x^4-30x^2+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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