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[Thread moved to homework forum by a Mentor]

the exercise was to find the roots of x^8 - 5x^6 + 7x^4 - 5x^2 +6=0

I substituded x^2 with y

: y^4 - 5y^3 + 7y^2 - 5y +6=0

I factored this by doing the rational roots test and trying those possible roots with the method of horner

and got (y-2) (y-3)(y^2+1)=0

with y=x^2 ---> (x^2-2) (x^2-3)(x^4+1)=0

i found the roots ±√2 , ±√3. which is correct and the answer on the back says these are the 2 anwsers. but (x^4+1) remains --> what are the 2 complex roots? how do I change 4^√-1 in a notation with i?

the exercise was to find the roots of x^8 - 5x^6 + 7x^4 - 5x^2 +6=0

I substituded x^2 with y

: y^4 - 5y^3 + 7y^2 - 5y +6=0

I factored this by doing the rational roots test and trying those possible roots with the method of horner

and got (y-2) (y-3)(y^2+1)=0

with y=x^2 ---> (x^2-2) (x^2-3)(x^4+1)=0

i found the roots ±√2 , ±√3. which is correct and the answer on the back says these are the 2 anwsers. but (x^4+1) remains --> what are the 2 complex roots? how do I change 4^√-1 in a notation with i?

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