what are the zeroes inclucing irrational of this polynomial? x^6 - 3x^3 - 10

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To find the zeros of the polynomial, we need to start with the transformation `z=x^3` .  

`x^6-3x^3-10`

`=z^2-3z-10`   now factor

`=(z-5)(z+2)`   put back to x

`=(x^3-5)(x^3+2)`

Each term has a real zero and two complex zeros.  The real zeros are given by

`x=5^{1/3}`

and 

`x=-2^{1/3}`

The real zeros of...

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To find the zeros of the polynomial, we need to start with the transformation `z=x^3` .  

`x^6-3x^3-10`

`=z^2-3z-10`   now factor

`=(z-5)(z+2)`   put back to x

`=(x^3-5)(x^3+2)`

Each term has a real zero and two complex zeros.  The real zeros are given by

`x=5^{1/3}`

and 

`x=-2^{1/3}`

The real zeros of the polynomial are `5^{1/3}` and `-2^{1/3}` .

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