Find roots of polynomial $$ p(x) = 10t+ \cancel{5t} -\cancel{5t}+1-t^3 $$
Answer
The roots of polynomial $ p(t) $ are:
$$ \begin{aligned}t_1 &= -0.1001\\[1 em]t_2 &= -3.111\\[1 em]t_3 &= 3.2111 \end{aligned} $$Explanation
Step 1:
Combine like terms:
$$ \color{blue}{10t} + \, \color{red}{ \cancel{5t}} \, \, \color{red}{ -\cancel{5t}} \,+1-t^3 = -t^3+ \color{red}{10t} +1 $$Step 2:
Polynomial $ -t^3+10t+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.
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