Obtain all other zeroes of the polynomial 2x3 -4x -x2 +2 , if two of its zeroes are root 2 and -root 2
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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 here ....
____________________________
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.
__________________________________
☺☺☺
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