quartic polynomial with no x-intercepts

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What is an example of a 4th degree polynomial with no x-intercepts. I have looked everywhere but can not find one.

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2 Answers

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Any quartic where terms of odd degree have zero coefficient,namely any quartic polynomial of form $f(x)=x^4+x^2+n$ where $n$ is any non-negative integer

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$y= x^4 - 12x^3 +59x^2 -138x +130$ is an example, as all of its roots are complex.

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