Question

6. Find all zeros of 2x^4 - 3x^3-3x^2 + 6x-2, if two of its zeros are 2 and -√2​

Answer 1

Since two zeroes are √2 and -√2, (x-√2)(x+√2)  =x2-2 is a  factor of the given polynomial. Now, we divide the given polynomial by x2 – 2.Read more on Sarthaks.com - https://www.sarthaks.com/250122/find-all-the-zeroes-of-2x-4-3x-3-3x-2-6x-2-if-you-know-that-two-of-its-zeroes-are-2-and-2

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So, 2x4 – 3x3 – 3x2 + 6x – 2 = (x2 – 2)(2x2 – 3x + 1). Now, by splitting –3x, we factorise 2x2 – 3x + 1 as (2x – 1)(x – 1). So, its zeroes are given by x =1/2 and x = 1. Therefore, the zeroes of the given polynomial are √2,-√2, 1/2,and find-all-the-zeroes-of-2x-4-3x-3-3x-2-6x-2-if-you-know-that-two-of-its-zeroes-are-2-and-2