document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976543>Question 976543</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How should I start this problem? \r<BR>\n" );
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document.write( "Find all rational zeros of the polynomial, and then find the irrational zeros, if any. Whenever appropriate, use the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule of Signs, the quadratic formula, or other factoring techniques. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.)\r<BR>\n" );
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document.write( "P(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E4+%2B+25x%5E2+%2B+6 ALIGN=MIDDLE  ALT=\"4x%5E4+%2B+25x%5E2+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598112 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4x^4 + 25x^2 +6=0<BR>\n" );
document.write( "(4x^2+1)(x^2+6)=0  Treat it like a quadratic.  Then see what the roots are.\r<BR>\n" );
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document.write( "4x^2=-1<BR>\n" );
document.write( "x^2=(-1/4)<BR>\n" );
document.write( "x=+/- (1/2)i\r<BR>\n" );
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document.write( "x^2=-6,  x= +/- I sqrt(6)\r<BR>\n" );
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document.write( "This should graph like a quadratic with +x^2, since as x increases negatively or positively, y increases without bound.  The y-intercept is (0,6), and there are no rational or irrational roots.  It won't touch the y-axis. The lowest value is at the y-intercept, since any positive or negative x will increase the value of the function from 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C2%2C-10%2C100%2C4x%5E4%2B25x%5E2%2B6%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C2%2C-10%2C100%2C4x%5E4%2B25x%5E2%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check  =1/16*1*4 + (-1)*25*(1/4)+6=(1/4)-6(1/4)+6=0<BR>\n" );
document.write( "i sqrt(6)^4=36<BR>\n" );
document.write( "i sqrt (6)=-6\r<BR>\n" );
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document.write( "4*36-25(-6)+6=0 </SPAN>\n" );
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