document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=15696>Question 15696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please can you help with this question:\r<BR>\n" );
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document.write( "Given that, for all values of x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the values of p,q and r </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7759 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=7759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given that, for all values of x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find the values of p,q and r<BR>\n" );
document.write( "  the given equation is a second degree polynomial in x and should have 2 roots or it should be satisfied by 2 values of x . but it is given that it is true for all values of x . so it is an identity . so coefficients of corresponding terms on either side of the identity shall be equal<BR>\n" );
document.write( "  l.h.s.=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x%5E2%2B12x%2B5 ALIGN=MIDDLE  ALT=\"f%28x%29=3x%5E2%2B12x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=r.h.s.=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%2Bq%29%5E2%2Br ALIGN=MIDDLE  ALT=\"p%28x%2Bq%29%5E2%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=px%5E2%2B2%2Ap%2Aq%2Ax%2Bp%2Aq%5E2%2Br ALIGN=MIDDLE  ALT=\"px%5E2%2B2%2Ap%2Aq%2Ax%2Bp%2Aq%5E2%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "hence 3=p<BR>\n" );
document.write( "     12 = 2p*q   or...... q=12/2*p = 12/2*3 = 12/6 =2<BR>\n" );
document.write( "     5= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2Aq%5E2%2Br ALIGN=MIDDLE  ALT=\"p%2Aq%5E2%2Br\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 3*2^2+r=12+r...or.....r=5-12 = -7<BR>\n" );
document.write( " </SPAN>\n" );
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