document.write( "Question 1026249: Explain whether or not there exists a third-degree polynomial with integer coefficients that has no real zeroes. \n" ); document.write( "

Algebra.Com's Answer #641475 by robertb(5830) $\"\"$ $\"About$

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There does NOT exist a 3rd degree polynomial with integer coefficients that has no real zeroes. The fact that if a pure complex number (one that contains \"i\") is a zero then guarantees its conjugate is also a zero implies that the third zero has to be without the imaginary unit i. (This is necessary, because the presence of the integer coefficients would force the absence of i for the 3rd zero.) \n" ); document.write( "

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