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

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)

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.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 2

Video Solution:

Obtain all other zeroes of 3x⁴ + 6x³ - 2x² - 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

Summary:

All the other zeroes of 3x⁴ + 6x³ - 2x² - 10x - 5, if two of its zeroes are √5/3 and -√5/3 are -1, and -1.

☛ Related Questions:

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