Find all the zeroes of the polynomial 3x^{4} + 6x^{3} - 2x^{2} - 10x - 5 if two of its zeroes are √(5/3) and – √(5/3)

### Answer

Since √(5/3) and – √(5/3) are the two zeroes therefore,

(x - √(5/3))(x + √(5/3)) = ^{1}/_{3}(3x^{2} - 5) is a factor of given polynomial.

Divide the given polynomial by 3x^{2} – 5.

For other zeroes, x^{2} + 2x + 1 = 0

(x + 1)^{2} = 0

x = –1, –1

Zeroes of the given polynomial are √(5/3), – √(5/3), –1 and –1.