document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=519317>Question 519317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
document.write( "\n" );
document.write( "The question states \"Find all rational zeros of f.  Then (if necessary) use the depressed equation to find all roots of the equations f(x)=0.\r<BR>\n" );
document.write( "\n" );
document.write( "3x^4-20x^3-20^x2-28x-7\r<BR>\n" );
document.write( "\n" );
document.write( "My possible zeros are +/- 1, 1/3, 7/3, 7.\r<BR>\n" );
document.write( "\n" );
document.write( "However none appear on the graph.  I am lost as to what to do next.  Thanks for the help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347788 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=347788\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The question states \"Find all rational zeros of f. Then (if necessary) use the depressed equation to find all roots of the equations f(x)=0. <BR>\n" );
document.write( "3x^4-20x^3-20^x2-28x-7 <BR>\n" );
document.write( "My possible zeros are +/- 1, 1/3, 7/3, 7.<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "Rational Roots Theorem:<BR>\n" );
document.write( "Synthetic Division<BR>\n" );
document.write( "...0...|....3......-20.......-20.......-28......-7.<BR>\n" );
document.write( "...1...|....3......-17.......-37.......-65......-72<BR>\n" );
document.write( "...2...|....3......-14.......-48.......-124....-131<BR>\n" );
document.write( "...3...|....3..............................................<BR>\n" );
document.write( "...4...|....3..............................................<BR>\n" );
document.write( "...5...|....3..............................................<BR>\n" );
document.write( "...6...|....3......-2.........-32......-220.....-1327<BR>\n" );
document.write( "...7...|....3........1.........-14......-126......-889 (sign switch on last number and all numbers>0)<BR>\n" );
document.write( "...8...|....3........4.......... 12.........68.........537 (8 is upper bound, and (7 < x < 8)<BR>\n" );
document.write( "...............................................................<BR>\n" );
document.write( "...0...|....3......-20.......-20.......-28......-7.  (sign switch on last number and all numbers alternate in sign)<BR>\n" );
document.write( "..-1..|....3......-23........3..........-31.......24 (-1 is lower bound, and (-1 < x < 0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "According to the Rational Roots Theorem as shown above, one real root is between 7 & 8, and the other real root is between -1 and 0. The other two roots should be non-real or imaginary.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "According to my graphics computer program, the two roots are irrational: 7.69567 and -0.242438.<BR>\n" );
document.write( "I don't no how to obtain these roots algebraically. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );