document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=563703>Question 563703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation whose roots are the reciprocals of the roots of the equation 5x^2 + 15x - 2= 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #364996 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=364996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Use the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{-15\ \pm\ \sqrt{225\ +\ 40}}{2(5)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_1\ =\ \frac{-15\ +\ \sqrt{265}}{10}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_2\ =\ \frac{-15\ -\ \sqrt{265}}{10}\">\r<BR>\n" );
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document.write( "Flip the fractions and rationalize the new denominators (see <a  rel=nofollow HREF=\"http://www.algebra.com/algebra/homework/Radicals/rationalizingdenominators1.lesson\">Rationalizing Denominators</a> if you need a refresher here)\r<BR>\n" );
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document.write( "To obtain:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_{1r}\ =\ \frac{-15\ +\ \sqrt{265}}{4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_{2r}\ =\ \frac{-15\ -\ \sqrt{265}}{4}\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ \left(\frac{-15\ +\ \sqrt{265}}{4}\right)\right)\ =\ 0\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ \left(\frac{-15\ -\ \sqrt{265}}{4}\right)\right)\ =\ 0\">\r<BR>\n" );
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document.write( "Hence\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ \left(\frac{-15\ +\ \sqrt{265}}{4}\right)\right)\left(x\ -\ \left(\frac{-15\ -\ \sqrt{265}}{4}\right)\right)\ =\ 0\">\r<BR>\n" );
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document.write( "First, simplfy the signs:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ +\ \left(\frac{15\ -\ \sqrt{265}}{4}\right)\right)\left(x\ +\ \left(\frac{15\ +\ \sqrt{265}}{4}\right)\right)\ =\ 0\">\r<BR>\n" );
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document.write( "Then use FOIL to multiply the two binomials.  Note that the second terms are a conjugate pair so their product is the difference of two squares.\r<BR>\n" );
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document.write( "Finally, multiply through by the denominator of the first degree and constant coefficients to write the equation with integer coefficients.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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