document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174303>Question 174303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many solutions does the polynomial have?<BR>\n" );
document.write( "How many real solution(s) does the polynomial have? <BR>\n" );
document.write( "Find all zeros of the polynomial? <BR>\n" );
document.write( "f(x)= x^3+x^2+2x+24 \r<BR>\n" );
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document.write( "**When i did this myself for the first question i put one and for the second question i put one and for the last question my answer was x= 2,-4,-3 but im not sure if it is right.** </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129241 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=129241\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the polynomial has a degree of 3 (x^3), it has three solutions. If you have to 'do it by hand', you can always find the 'possible' real answers by looking at the factors of the coefficients that make up the high order term and the lowest order term. Since the high order temr is one, the possible real answers will be +_<BR>\n" );
document.write( "1,2,3,4,6,8,12,24 . Then you just use trial and error to find that -3 works\r<BR>\n" );
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document.write( "Use this URL first --> http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic\r<BR>\n" );
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document.write( "From that answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x%5E2-2x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x%5E2-2x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > you see there is one real answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then use the quadratic equation to find the other two<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-2x%2B8+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2x%2B8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-2%29%5E2-4%2A1%2A8=-28 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2%29%5E2-4%2A1%2A8=-28\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -28 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -28 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+28%29+=+5.29150262212918 ALIGN=MIDDLE  ALT=\"sqrt%28+28%29+=+5.29150262212918\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28--2%2B-+i%2Asqrt%28+-28+%29%29%2F2%5C1+=++%28--2%2B-+i%2A5.29150262212918%29%2F2%5C1+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B8+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B8+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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