Obtain all other zeroes of `3x^4+6x^3-2x^2-10 x-5`, if two of its zeroes are `sqrt(5/3)`and `-sqrt(5/3)`.

Explanation

To find all the zeroes of the polynomial \( P(x) = 3x^4 + 6x^3 - 2x^2 - 10x - 5 \), given that two of its zeroes are \( \sqrt{\frac{5}{3}} \) and \( -\sqrt{\frac{5}{3}} \), we can follow these steps:

### Step 1: Identify the known zeroes and their factors
The two known zeroes are \( \alpha = \sqrt{\frac{5}{3}} \) and \( \beta = -\sqrt{\frac{5}{3}} \). The corresponding factors of the polynomial are:
\[ (x - \sqrt{\frac{5}{3}}) \quad \text{and} \quad (x + \sqrt{\frac{5}{3}}) \]
We can combine these factors to form a quadratic factor:
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