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How can I proof the statement below by contradiction? If n is an odd natural number, then the equation 4+(x+1)(nx+x^2)=nx has no rational roots. *Does

How can I proof the statement below by contradiction?

If n is an odd natural number, then the equation 4+(x+1)(nx+x^2)=nx has no rational roots.

*Does the solution involve with solving quintic polynomials? The only way I know how to solve polynomials is by splitting it into linear factors, so I am quite lost here...

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