document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129742>Question 1129742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> do all the roots of the polynomial x^5-4x^4-7x^3+14x^2-44x+120 make sense in regards to a roller coaster engineering project problem.explain why or why not in a complete sentence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746332 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> breakdown to the exact value of the roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5-2x%5E4-2x%5E4-11x%5E3%2B4x%5E3%2B22x%5E2-8x%5E2-60x%2B16x%2B120=0 ALIGN=MIDDLE  ALT=\"x%5E5-2x%5E4-2x%5E4-11x%5E3%2B4x%5E3%2B22x%5E2-8x%5E2-60x%2B16x%2B120=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%5E4-2x%5E3-15x%5E2%2B4x%5E2-8x-60%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%5E4-2x%5E3-15x%5E2%2B4x%5E2-8x-60%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28%28x%5E4%2B4x%5E2%29-%282x%5E3%2B8x%29-%2815x%5E2%2B60%29%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28%28x%5E4%2B4x%5E2%29-%282x%5E3%2B8x%29-%2815x%5E2%2B60%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+2%29+%28x+%2B+3%29+%28x+-+5%29+%28x%5E2+%2B+4%29=0 ALIGN=MIDDLE  ALT=\"%28x+-+2%29+%28x+%2B+3%29+%28x+-+5%29+%28x%5E2+%2B+4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the coaster returns to ground level at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the three real zeros of the function\r<BR>\n" );
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document.write( "do all the roots of the polynomial <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5-4x%5E4-7x%5E3%2B14x%5E2-44x%2B120 ALIGN=MIDDLE  ALT=\"x%5E5-4x%5E4-7x%5E3%2B14x%5E2-44x%2B120\"   DISABLED_style= \"max-width:90%; height:auto;\" > make sense in regards to a roller coaster engineering project problem????\r<BR>\n" );
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document.write( "the roots of the polynomial mathematically make sense in regards to a roller coaster engineering project problem because these values (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) mean the ride starts on the ground\r<BR>\n" );
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document.write( "but, mathematical end behavior of this function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=does ALIGN=MIDDLE  ALT=\"does\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=make ALIGN=MIDDLE  ALT=\"make\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sense+ ALIGN=MIDDLE  ALT=\"sense+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+practically ALIGN=MIDDLE  ALT=\"+practically\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "function has local maximum and minimum where first derivative is equal to zero:\r<BR>\n" );
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document.write( "and it is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+x%5E4+-+16+x%5E3+-+21+x%5E2+%2B+28+x+-+44=0 ALIGN=MIDDLE  ALT=\"5+x%5E4+-+16+x%5E3+-+21+x%5E2+%2B+28+x+-+44=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > at\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-1.89 ALIGN=MIDDLE  ALT=\"x=+-1.89\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.03 ALIGN=MIDDLE  ALT=\"x=4.03\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, function is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28Increasing%29 ALIGN=MIDDLE  ALT=\"highlight%28Increasing%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.89 ALIGN=MIDDLE  ALT=\"-1.89\"   DISABLED_style= \"max-width:90%; height:auto;\" >),(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.03 ALIGN=MIDDLE  ALT=\"4.03\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28Decreasing%29 ALIGN=MIDDLE  ALT=\"highlight%28Decreasing%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.89 ALIGN=MIDDLE  ALT=\"-1.89\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.03 ALIGN=MIDDLE  ALT=\"4.03\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-250%2C+250%2C%28x+-+2%29+%28x+%2B+3%29+%28x+-+5%29+%28x%5E2+%2B+4%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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