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

Two zeroes of ( 3x⁴ + 6x³ - 2x² - 10x - 5 ) are √5/3 and -√5/3 which means that is a factor of ( 3x⁴ + 6x³ - 2x² - 10x - 5 ).

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

we factorize x² + 2x + 1 = (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 2 zeros at x = - 1.

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