Write the coeeficientes of the polynomial in order:
| 1 - 5 6 - 30
|
|
|
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After some trials you probe with 5
| 1 - 5 6 - 30
|
|
5 | 5 0 30
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1 0 6 0 <---- residue
Given that the residue is 0, 5 is a root.
The quotient is x^2 + 6 = 0, which does not have a real root.
Therefore, 5 is the only root. You can prove it by solving the polynomial x^2 + 6 = 0.
