document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173792>Question 173792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the roots of x^2+px+q=0 are (alpha) and 4(alpha) show that 4p^2= 25q. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128853 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=128853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The roots of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bpx%2Bq=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bpx%2Bq=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4alpha ALIGN=MIDDLE  ALT=\"4alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-alpha%29 ALIGN=MIDDLE  ALT=\"%28x-alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4alpha%29 ALIGN=MIDDLE  ALT=\"%28x-4alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bpx%2Bq ALIGN=MIDDLE  ALT=\"x%5E2%2Bpx%2Bq\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-alpha%29%28x-4alpha%29=x%5E2-%28alpha%2B4alpha%29%2B4alpha%5E2=x%5E2-5alpha%2Ax%2B4alpha%5E2=x%5E2%2Bpx%2Bq ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-5alpha ALIGN=MIDDLE  ALT=\"p=-5alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q=4alpha%5E2 ALIGN=MIDDLE  ALT=\"q=4alpha%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%5E2=4%28-5alpha%29%5E2=4%2A25alpha%5E2=100alpha%5E2 ALIGN=MIDDLE  ALT=\"4p%5E2=4%28-5alpha%29%5E2=4%2A25alpha%5E2=100alpha%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25q=25%2A4alpha%5E2=100alpha%5E2 ALIGN=MIDDLE  ALT=\"25q=25%2A4alpha%5E2=100alpha%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "QED </SPAN>\n" );
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