what are the zeroes inclucing irrational of this polynomial? x^4 + 2x^2 - 15

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To find the zeros of this polynomial, use the transformation `z=x^2` .  This means that the polynomial becomes:

`x^4+2x^2-15`

`=z^2+2z-15`   factor

`=(z+5)(z-3)`   now go back to x

`=(x^2+5)(x^2-3)`   the first term has complex roots, the second irrational

`=(x^2+5)(x-sqrt3)(x+sqrt3)`

The real zeros of the polynomial are `sqrt3` and `-sqrt3` .

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To find the zeros of this polynomial, use the transformation `z=x^2` .  This means that the polynomial becomes:

`x^4+2x^2-15`

`=z^2+2z-15`   factor

`=(z+5)(z-3)`   now go back to x

`=(x^2+5)(x^2-3)`   the first term has complex roots, the second irrational

`=(x^2+5)(x-sqrt3)(x+sqrt3)`

The real zeros of the polynomial are `sqrt3` and `-sqrt3` .

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