document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177572>Question 1177572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation x²+ px +4 = 0, where p and q are constants, has roots -1 and 4. a) Find the values of p and q.\r<BR>\n" );
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document.write( "b) Using these values of p and q. find the value of r, where r is a constant, and the equation x² + px + r=0 has equal roots. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806642 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=806642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" > is missing from given equation, so I assume you have<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2B+px+%2B4q+=+0 ALIGN=MIDDLE  ALT=\"+x%5E2%2B+px+%2B4q+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) Find the values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "use the rule: sum of the roots = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2Fa+ ALIGN=MIDDLE  ALT=\"-b%2Fa+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2B4=3 ALIGN=MIDDLE  ALT=\"-1%2B4=3\"   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=-b%2Fa+=3 ALIGN=MIDDLE  ALT=\"-b%2Fa+=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=p ALIGN=MIDDLE  ALT=\"b=p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%2F1+=3 ALIGN=MIDDLE  ALT=\"-p%2F1+=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-3 ALIGN=MIDDLE  ALT=\"p=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "product of the roots =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%2Fa ALIGN=MIDDLE  ALT=\"+c%2Fa\"   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=c=4q ALIGN=MIDDLE  ALT=\"c=4q\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   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=4q%2F1=%28-1%29%2A4 ALIGN=MIDDLE  ALT=\"4q%2F1=%28-1%29%2A4\"   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=4q=-4 ALIGN=MIDDLE  ALT=\"4q=-4\"   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=q=-1 ALIGN=MIDDLE  ALT=\"q=-1\"   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=+x%5E2-3x+-4+=+0 ALIGN=MIDDLE  ALT=\"+x%5E2-3x+-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) Using these values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+ ALIGN=MIDDLE  ALT=\"p+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   DISABLED_style= \"max-width:90%; height:auto;\" > find the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a constant, and the equation <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B+px+%2B+r=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B+px+%2B+r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equal ALIGN=MIDDLE  ALT=\"equal\"   DISABLED_style= \"max-width:90%; height:auto;\" > roots \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-3 ALIGN=MIDDLE  ALT=\"p=-3\"   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=x%5E2-3x+%2B+r=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x+%2B+r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....if equation has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equal ALIGN=MIDDLE  ALT=\"equal\"   DISABLED_style= \"max-width:90%; height:auto;\" > roots, write left side as square of difference<BR>\n" );
document.write( "sum of the roots <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2Fa+=-%28-3%29%2F1+=3 ALIGN=MIDDLE  ALT=\"-b%2Fa+=-%28-3%29%2F1+=3\"   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=x%5B1%5D%2Bx%5B2%5D=3 ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............eq.1. since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B+px+%2B+r=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B+px+%2B+r=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equal ALIGN=MIDDLE  ALT=\"equal\"   DISABLED_style= \"max-width:90%; height:auto;\" > roots, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D=x%5B2%5D\"   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=2x%5B1%5D=3 ALIGN=MIDDLE  ALT=\"2x%5B1%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=3%2F2 ALIGN=MIDDLE  ALT=\"x%5B1%5D=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "product of the roots =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c%2Fa=r%2F1=r ALIGN=MIDDLE  ALT=\"+c%2Fa=r%2F1=r\"   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=x%5B1%5D%2Ax%5B1%5D=r ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Ax%5B1%5D=r\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29%2A%283%2F2%29=r ALIGN=MIDDLE  ALT=\"%283%2F2%29%2A%283%2F2%29=r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=9%2F4 ALIGN=MIDDLE  ALT=\"r=9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and your equatio is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x+%2B+9%2F4=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x+%2B+9%2F4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );