document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62016>Question 62016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P(x)=x^4-4x^3-4x^2-4x-5 it aks me to find all rational zeros of the polynomial. but i dont really know what te rational numbers are<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 #42746 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=42746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x)=x^4-4x^3-4x^2-4x-5 it aks me to find all rational zeros <BR>\n" );
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document.write( "x=-1 is one of the rational zeroes.<BR>\n" );
document.write( "Dividing P(x) by x+1 you get a quotient <BR>\n" );
document.write( "of x^3-5x^2+x-5.<BR>\n" );
document.write( "This cubic has a rational zero of x=5<BR>\n" );
document.write( "Dividing it by x-5 you get a quotient <BR>\n" );
document.write( "of x^2+1 which has complex zeroes.<BR>\n" );
document.write( "So the rational zeroes are x=1, x=5.<BR>\n" );
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document.write( "Comment: Rational numbers are any number<BR>\n" );
document.write( "which can be written as the ratio of two<BR>\n" );
document.write( "integers.  Irrational zeroes cannot be <BR>\n" );
document.write( "expressed in this way.  For example sqrt2<BR>\n" );
document.write( "pi, cube root of 5: these are all irrational.Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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