document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026249>Question 1026249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain whether or not there exists a third-degree polynomial with integer coefficients that has no real zeroes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641476 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39792)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=641476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you found this example,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B6%29%28x%5E2%2B5%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B6%29%28x%5E2%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you would understand that this has only a single real zero, while the other TWO zeros are not real.  The degree of the equation, if as a function, is odd, specifically here, being 3.  NOT even, but odd.  Could you imagine any such <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-a%29%28x%5E2%2Bb%29 ALIGN=MIDDLE  ALT=\"y=%28x-a%29%28x%5E2%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which the root x-a would be not Real?  Assuming a and b are Real... </SPAN>\n" );
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