# Obtain all other zeroes of 3x^{4} + 6x^{3} - 2x^{2} - 10x - 5, if two of its zeroes are √(5/3) and -√(5/3)

**Solution:**

Given polynomial p(x) = 3x^{4} + 6x^{3} - 2x^{2} - 10x - 5

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

Therefore,

[x - √(5/3)] [x + √(5/3)] = [x^{2} - 5/3] is a factor of 3x^{4} + 6x^{3} - 2x^{2} - 10x - 5

Therefore, we divide the given polynomial by( x^{2} - 5/3)

Therefore, 3x^{4} + 6x^{3} - 2x^{2} - 10x - 5 = (x^{2} - 5/3)(3x^{2} + 6x + 3) + 0

= 3 (x^{2} - 5/3) (x^{2} + 2x + 1)

We factorize x^{2} + 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 two identical zeroes at x = - 1

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

**Video Solution:**

## Obtain all other zeroes of 3x^{4} + 6x^{3} - 2x^{2} - 10x - 5, if two of its zeroes are √(5/3) and -√(5/3)

### NCERT Solutions Class 10 Maths - Chapter 2 Exercise 2.3 Question 3:

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

The zeroes of the given polynomial 3x^{4} + 6x^{3} - 2x^{2} - 10x - 5 are √(5/3), -√(5/3), -1, and -1