Find roots of polynomial $$ p(x) = x^3-12x+48x-63 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.6298\\[1 em]x_2 &= -0.8149+6.1638i\\[1 em]x_3 &= -0.8149-6.1638i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ x^3 \color{blue}{-12x} + \color{blue}{48x} -63 = x^3+ \color{blue}{36x} -63 $$Step 2:
Polynomial $ x^3+36x-63 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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