find all the zeroes of 2x^4-3x^-3x^2+6x-2 ,it is given that two of its zero are root 2 and-root 2
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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
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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 1.
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