document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020839>Question 1020839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> h(x)= 3x^4+17x^3+10x^2+x+5 \r<BR>\n" );
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document.write( "The function below has at least one rational zero. Use this fact to find all zeros of the function. The function below has at least one rational zero. Use this fact to find all zeros of the function. If there is more than one zero separate them with commas. Write exact values not decimal approximations. \r<BR>\n" );
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document.write( " Thank you!!!!!!!!!!!!!! I hate math!! :-(  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636688 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By the rational root theorem, the rational root is of the form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large x = \pm \frac{p}{q}\">\r<BR>\n" );
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document.write( "where p and q are positive integers and p is a factor of 5, q is a factor of 3. Moreover, the root must be negative (since all coefficients are positive, so it can't possibly have a positive root). So you only need to check -1/1, -1/3, -5/1, and -5/3.\r<BR>\n" );
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document.write( "Once you have found the rational root x_0, divide by (x - x_0) to obtain a 3rd degree polynomial. The 3rd degree polynomial must have a rational root; if it is rational, then you can use the rational root theorem again, otherwise you might need to use a calculator. Once you have found the second root, divide again to obtain a quadratic polynomial, in which you can solve using the quadratic formula. </SPAN>\n" );
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