Question

Obtain all the zeroes of the polinomial, 2x cube - 4x - x square + 2 , if two of its zeroes are, √2 and √-2 ?

Answer 1

Answer:

The polynomial is 2x³ - x² - 4x + 2

Given, √2 and -√2 are the two zeroes.

So, (x - √2) and (x- -√2) are the factors.

i. e., (x-√2) and (x+√2) are the factors.

So, (x-√2)(x+√2) is also a factor.

i. e., x² - (√2)² is a factor.

= x² - 2

Then we want to divide the polynomial with x² - 2

_2x___-__1_____

x² - 2 | 2x³ - x² - 4x + 2

| 2x³ - 4x

______________

- x² + 2

-x² + 2

_______________

0

2x - 1 = 0

2x = 1

x = 1/2