Question

Find all the zeros for 2 x power 4 minus 3 x power 3 minus 3 x power 2 + 6 x minus 2 given two of its zero root 2 and minus root 2

Answer 1

p(x) = 2x^4 -3x³ - 3x² + 6x - 2 
given, √2 and -√2 are the zeroes of the polynomial
therefore, (x-√2) and (x+√2) are the factors
(multiplying both)
(x^2-2) is a factor
by dividing the polynomial (see the attachment) we get,

2x² - 3x + 1

=> 2x² - 2x - x + 1

=> 2x( x - 1) - 1( x - 1)


=> ( x -1) (2x - 1)

∴ ( x - 1 )= 0

∴ x = 1

and 

∴ (2x -1) = 0

∴ 2x = 1

∴ x = 1/2

Therefore, the zeroes of the given polynomial are 1 , 1/2 , √2 and -√2 .
hope it helps:)

Answer 2

Answer:

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