Question

find all the other zeroes of the polyno ial 2x^4-3x^3+6x-2 if two of its zeroes are root 2 and -root 2 ​

Answer 1

Answer:

Since two zeroes are √2 and -√2 x-√2x+√2 =x2-2 is a factor of the given polynomial. Now we divide the given polynomial by x2 – 2.So 2x4 – 3x3 – 3x2 + 6x – 2 = x2 – 22x2 – 3x + 1.Now by splitting –3x we factorise 2x2 – 3x + 1 as 2x – 1x – 1. So its zeroesare given by x =1/2 and x = 1. Therefore the zeroes of the given polynomial are √2 -√2 1/2 and 1.