document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22955>Question 22955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by factoring--4xcubed - 28xsquared + 49x > 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11325 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First you need to figure out where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E3+-+28x%5E2+%2B+49x+=+0 ALIGN=MIDDLE  ALT=\"4x%5E3+-+28x%5E2+%2B+49x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, lets do this...\r<BR>\n" );
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document.write( "so either x=0 or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+28x+%2B+49+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2+-+28x+%2B+49+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The second polynomial factorises futher to (2x-7)(2x-7) = 0, which means 2x = 7. In other words x = 7/2.\r<BR>\n" );
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document.write( "So there are 2 \"roots\" (where y=0): at x=0 and x=7/2.\r<BR>\n" );
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document.write( "The question asks where is the polynomial GREATER than zero. To answer this, you need to be able to sketch (not plot) the graph quickly. You need to know what a cubic looks like first and then apply that knowledge to the info you have.\r<BR>\n" );
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document.write( "The cubic looks like: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C+300%2C+-1%2C+7%2C+-10%2C+30%2C+4x%5E3+-+28x%5E2+%2B+49x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C+300%2C+-1%2C+7%2C+-10%2C+30%2C+4x%5E3+-+28x%5E2+%2B+49x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, looking at the graph, where is the curve GREATER than zero? it is greater than zero when x>0 but not at the point x=7/2 --> here it is equal to zero.\r<BR>\n" );
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document.write( "So, answer is 0 < x < 7/2 and x > 7/2 <BR>\n" );
document.write( "OR x>0, but not x=7/2\r<BR>\n" );
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document.write( "Both say the same thing\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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