Find roots of polynomial $$ p(x) = 7+5x^4-3x^2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.8612+0.6645i\\[1 em]x_2 &= 0.8612-0.6645i\\[1 em]x_3 &= -0.8612+0.6645i\\[1 em]x_4 &= -0.8612-0.6645i \end{aligned} $$Explanation
Step 1:
Write polynomial in descending order
$$ \begin{aligned} 7+5x^4-3x^2 & = 0\\[1 em] 5x^4-3x^2+7 & = 0 \end{aligned} $$Step 2:
Polynomial $ 5x^4-3x^2+7 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.
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