Determine the roots of the given cubic equation:
$q^{3}-1 q^{2}-25 q+25=0$

Answer

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Answer

Final Answer: The roots of the given cubic equation are $\boxed{-5}$, $\boxed{5}$, and $\boxed{1}$.

Steps

Step 1 ：We are given the cubic equation $q^{3}-1 q^{2}-25 q+25=0$.

Step 2 ：We need to find the roots of this equation. The roots are the values of $q$ for which the equation becomes zero.

Step 3 ：Using a mathematical software, we find that the roots of the equation are -5, 5, and 1.

Step 4 ：Final Answer: The roots of the given cubic equation are $\boxed{-5}$, $\boxed{5}$, and $\boxed{1}$.