document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177786>Question 1177786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> https://gyazo.com/911d576522641918b00f6e16b83a5956 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806882 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=806882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor has nothing to do with the question that is asked.<br><BR>\n" );
document.write( "Her response is about PAIRS of equations which have no COMMON SOLUTION.  The question is about single polynomial equations that have no REAL ROOTS.<br><BR>\n" );
document.write( "A polynomial equation of odd degree will always have at least one real solution, because the end behavior for large positive x is different than for large negative x.<br><BR>\n" );
document.write( "A polynomial equation of even degree does not need to have a real root, because the end behavior for large positive x and for large negative x is the same.  If a polynomial equation of even degree has all coefficients positive, then every term will be positive and the equation will have no real solutions; and likewise if all terms have negative coefficients.<br><BR>\n" );
document.write( "Here are graphs of two polynomial equations with no real solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E2%2B3 ALIGN=MIDDLE  ALT=\"y=x%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x%5E4-2x%5E2-1 ALIGN=MIDDLE  ALT=\"y=-x%5E4-2x%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-3%2C3%2C-40%2C40%2Cx%5E2%2B3%2C-x%5E4-2x%5E2-1%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-3%2C3%2C-40%2C40%2Cx%5E2%2B3%2C-x%5E4-2x%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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