document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=907261>Question 907261</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I solve this polynomial inequality and put the solution set into interval notation?\r<BR>\n" );
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document.write( "9x^2 + 1 is greater than or equal to 6x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550240 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=550240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2%2B1%3E=6x ALIGN=MIDDLE  ALT=\"9x%5E2%2B1%3E=6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-6x%2B1%3E=0 ALIGN=MIDDLE  ALT=\"9x%5E2-6x%2B1%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Roots are these.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286-sqrt%2836-4%2A9%2A1%29%29%2F18 ALIGN=MIDDLE  ALT=\"%286-sqrt%2836-4%2A9%2A1%29%29%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2Bsqrt%2836-4%2A9%2A1%29%29%2F18 ALIGN=MIDDLE  ALT=\"%286%2Bsqrt%2836-4%2A9%2A1%29%29%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > which are equal because the discriminant is 0.<BR>\n" );
document.write( "Only one root:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F18=1%2F3 ALIGN=MIDDLE  ALT=\"6%2F18=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The inequality is true for all real values of x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-4%2C4%2C-2%2C4%2C9x%5E2-6x%2B1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-4%2C4%2C-2%2C4%2C9x%5E2-6x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You could factorize the quadratic trinomial, since you found the single root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Not so easy to recognize without actually evaluating the discriminant.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28x%5E2-%286%2F9%29x%2B1%2F9%29%3E=0 ALIGN=MIDDLE  ALT=\"9%28x%5E2-%286%2F9%29x%2B1%2F9%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289%28x-1%2F3%29%5E2%3E=0%29 ALIGN=MIDDLE  ALT=\"highlight%289%28x-1%2F3%29%5E2%3E=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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