document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=45236>Question 45236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this problem? I have no idea how to find any of the zeros!!!\r<BR>\n" );
document.write( "\n" );
document.write( "Find a rational zero of the polynomial function f(x)=3x^3 - 17x^2 + 18x +8, then use it to find all the zeros of the function.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thank You!!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #30030 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=30030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do you have a graphing calculator?  If so, then you can graph the function, and see where it crosses the x axis.  These would be zeros of the rational function (actually it is a polynomial function!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C300%2C+-2%2C5%2C+-10%2C10%2C+3x%5E3+-+17x%5E2+%2B+18x+%2B8%29+ ALIGN=MIDDLE  ALT=\"graph+%28300%2C300%2C+-2%2C5%2C+-10%2C10%2C+3x%5E3+-+17x%5E2+%2B+18x+%2B8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "From the graph above, you can see that there are zeros at x = 2 and x=4, with a third root at x=-1/3.  Since the polynomial is of degree 3, there are only three roots, so this must be the three roots:  x = -1/3, 2, and 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You can verify these roots by synthetic division by either 2 or 4 (or -1/3 I suppose!), which will give you a reduced equation that is quadratic.  This quadratic equation can be solved by factoring.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "NOTE:  This is NOT the traditional way to solve this problem.  The great French mathematician Rene Descartes is either VERY PROUD of us, or he is turning over in his grave!!\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R^2 at SCC<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );