Question

obtain all other zeroes of the polynomial 2xcube-4x-xsquare,if two of its zeroes are under root 2and- under root 2
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Answer 1

Answer:

The Given Polynomial is f(x) = 2x^3 - 4x - x^2 +2.

since √2 and -√2 are the zeroes of f(x) , it follows that each one of ( x - √2 ) and ( x + √2 )

is a factor of f (x ).

CONSEQUENTLY , (x - √2)(x+√2) =(x^2 - 2 ) is a factor of f (x).

on dividing f (x ) = 2x^3 - x^2 - 4x + 2 by x^2 - 2 , we get

=> f (x) = 0

=> (x^2 - 2)(2x-1)=0

=>(x - √2) (x + √2) (2x - 1 )=0

=> (x - √2 )=0 or (x + √2 ) =0 or (2x - 1 )=0

=> x = √2 or x = -√2 or x = 1/2.

HENCE , all zeroes of f(x) are √2 , -√2 and 1/2.

Answer 2

Hey mate your answer is in the given attachment

HOPE IT IS HELPFUL ....... ;)☆