Find roots of polynomial $$ p(x) = -17x^3+8x^2+34-16 $$
Answer
The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2027\\[1 em]x_2 &= -0.366+0.864i\\[1 em]x_3 &= -0.366-0.864i \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ -17x^3+8x^2+ \color{blue}{34} \color{blue}{-16} = -17x^3+8x^2+ \color{blue}{18} $$Step 2:
Polynomial $ -17x^3+8x^2+18 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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