Step-by-step explanation:

Solution:

Given polynomial p(x) = 3x4 + 6x3 - 2x2 - 10x - 5

Two zeroes of the polynomial are given as √(5/3) and -√(5/3)

Therefore,

[x - √(5/3)] [x + √(5/3)] = (x2 - 5/3) is a factor of 3x4 + 6x3 - 2x2 - 10x - 5.

Therefore, we divide the given polynomial by (x2 - 5/3)

Obtain all other zeroes of 3x⁴ + 6x³ - 2x² - 10x - 5, if two of its zeroes are √5/3 and -√5/3

Therefore, 3x4 + 6x3 - 2x2 - 10x - 5 = (x2 - 5/3)(3x2 + 6x + 3) + 0

= 3 (x2 - 5/3) (x2 + 2x + 1)

On factorizing x2 + 2x + 1, we get (x + 1)2

Therefore, its zero is given by

x + 1 = 0

x = - 1

As it has the term (x + 1)2,

Therefore, there will be two identical zeroes at x = - 1

Hence the zeroes of the given polynomial are √(5/3) and -√(5/3), - 1 and - 1.