Find roots of polynomial $$ p(x) = x^4+5-2 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9306+0.9306i\\[1 em]x_2 &= 0.9306-0.9306i\\[1 em]x_3 &= -0.9306+0.9306i\\[1 em]x_4 &= -0.9306-0.9306i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^4+ \color{blue}{5} \color{blue}{-2} = x^4+ \color{blue}{3} $$Step 2:
Polynomial $ x^4+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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