Find roots of polynomial $$ p(x) = 3x^3-10x+7x+3 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.3247\\[1 em]x_2 &= 0.6624+0.5623i\\[1 em]x_3 &= 0.6624-0.5623i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ 3x^3 \color{blue}{-10x} + \color{blue}{7x} +3 = 3x^3 \color{blue}{-3x} +3 $$Step 2:
Polynomial $ 3x^3-3x+3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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