document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984208>Question 984208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can I determine the zeros roots and interceptors of this third-degree polynomial function f ( x ) = x ^ 3 + x ^ 2-4x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #604992 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=604992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28+x+%29=0 ALIGN=MIDDLE  ALT=\"f+%28+x+%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=0=+x%5E3+%2B+x%5E2-4x ALIGN=MIDDLE  ALT=\"0=+x%5E3+%2B+x%5E2-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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=0+=+x%28x%5E2%2Bx-4%29 ALIGN=MIDDLE  ALT=\"0+=+x%28x%5E2%2Bx-4%29\"   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=0+=+highlight%28x%29highlight%28%28x%5E2%2Bx-4%29%29 ALIGN=MIDDLE  ALT=\"0+=+highlight%28x%29highlight%28%28x%5E2%2Bx-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >... this product will be equal to zero only if one or both of the factors is equal to zero\r<BR>\n" );
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document.write( "so, one root is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B1%5D=0%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B1%5D=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the other two roots we will get solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx-4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   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=x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+\"   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=x+=+%28-1+%2B-+sqrt%28+1%2B16+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%2B16+%29%29%2F2+\"   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=x+=+%28-1+%2B-+sqrt%28+17+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+17+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "exact solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B2%5D+=+%28-1+%2B+sqrt%28+17+%29%29%2F2%29+ ALIGN=MIDDLE  ALT=\"highlight%28x%5B2%5D+=+%28-1+%2B+sqrt%28+17+%29%29%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B3%5D+=+%28-1+-+sqrt%28+17+%29%29%2F2%29+ ALIGN=MIDDLE  ALT=\"highlight%28x%5B3%5D+=+%28-1+-+sqrt%28+17+%29%29%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );