document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463055>Question 463055</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of p if the roots of the quadratic equation 4x^2-(5p+1)x+5p=0 differ by 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317368 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=317368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note that the roots of the quadratic are in the form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE r_1, r_2 = \frac{-(5p+1) \pm \sqrt{(5p+1)^2 - 4(4)(5p)}}{8}  = \frac{-5p - 1}{8} \pm \frac{\sqrt{25p^2 - 70p + 1}}{8}\"> (upon simplification). If we want these roots to differ by 1, we need to set the equality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{\sqrt{25p^2 - 70p + 1}}{8} = \frac{1}{2}\">\r<BR>\n" );
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document.write( "This is so that the roots will be in the form k + (1/2) and k - (1/2), differing by 1. Solving this equation for p,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sqrt{25p^2 - 70p + 1} = 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 25p^2 - 70p + 1 = 16\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 25p^2 - 70p - 15 = 0\"> Luckily, this factors:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 5(5p + 1)(p - 3) = 0\">\r<BR>\n" );
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document.write( "p = -1/5 or p = 3. </SPAN>\n" );
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