What are all the possible rational zeros for f(x)=x^6-64?

daliner4jl

daliner4jl

Answered question

2023-02-11

What are all the possible rational zeros for f ( x ) = x 6 - 64

Answer & Explanation

Jamya Reid

Jamya Reid

Beginner2023-02-12Added 7 answers

Only "possible" rational zeros are ± 1 , ± 2 , ± 4 , ± 8 , ± 16 , ± 32 , ± 64
x 6 - 64 = ( ( x 3 ) 2 - 8 2 )
x 6 - 64 = ( x 3 - 8 ) ( x 3 + 8 )
x 6 - 64 = ( x 3 - 2 3 ) ( x 3 + 2 3 )
x 6 - 64 = ( x - 2 ) ( x 2 + 2 x + 4 ) ( x + 2 ) ( x 2 - 2 x + 4 )
Rational zeros x=-+2
x 2 - 2 x + 4 = ( x - 1 - 3 i ) ( x - 1 + 3 i )
Complex zeros x = - 1 ± 3 i and x = 1 ± 3 i

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