If `x - sqrt(5)` is a factor of the cubic polynomial `x^(3)-3sqrt(5)x^(2)+13x - 3sqrt(5)`, then find all the zeroes of the polynomial.

Explanation

To find all the zeroes of the cubic polynomial \( P(x) = x^3 - 3\sqrt{5}x^2 + 13x - 3\sqrt{5} \), given that \( x - \sqrt{5} \) is a factor, we can follow these steps:

### Step 1: Identify the known zero
Since \( x - \sqrt{5} \) is a factor, it means that \( \sqrt{5} \) is a zero of the polynomial. Therefore, we can say:
\[ P(\sqrt{5}) = 0 \]

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