obtain all zeroes of the polynomial 2x^4-3x^3-3x^2+6x+2 if two zeroes are √2 and -√2
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the given polynomial is wrong
(2x^4-3x^3-3x^2+6x-2) will be the correct polynomial
other two zeroes will be 1/2 and 1
Step-by-step explanation:
since -√2 and √2 are the zeroes of the polynomial then( x-2) and (x+2) must be the factor of it
hence, x^2-2 will be the factor of it.
on dividing polynomial by x^2-2 , we get
(2x^4-3x^3-3x^2+6x-2)/x^2-2
quotient= 2x^2-3x+1
remainder=0
2x^2-3x+1=0
2x^2-2x-x+1 =0
2x(x-1) -1(x-1) =0
(2x-1)(x-1)=0
hence, x= 1/2 or 1
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