document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43157>Question 43157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all real zeros of the function given below.<BR>\n" );
document.write( "f(x) = x3 - 8x - 3\r<BR>\n" );
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document.write( "  a. rational zero at x = -3<BR>\n" );
document.write( "irrational zeros at x = 5.23 and x = 0.76    <BR>\n" );
document.write( "  b. rational zero at x = 3<BR>\n" );
document.write( "irrational zeros at x = -0.38 and x = -2.62    <BR>\n" );
document.write( "  c. rational zero at x = -3<BR>\n" );
document.write( "irrational zeros at x = 2.62 and x = 0.38    <BR>\n" );
document.write( "  d. rational zero at x = 3<BR>\n" );
document.write( "irrational zeros at x = -0.76 and x = -5.23    <BR>\n" );
document.write( "  e. None of the others    <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 #28198 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=28198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^3 - 8x - 3 \r<BR>\n" );
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document.write( "f(3)=27-24-3, so 3 is a zero\r<BR>\n" );
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document.write( "x-3 is a factor as is x^2+3x+1\r<BR>\n" );
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document.write( "The zeroes of this quadratic are:\r<BR>\n" );
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document.write( "x=[-3+sqrt(3^2-4)]/2 or x=[-3-sqrt(3^2-4)]/2<BR>\n" );
document.write( "x=[-3+sqrt5]/2 or x=[-3-sqrt5]/2\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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