document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=940400>Question 940400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the value of p if the equations 3x^2-2x+p=0 and 6x^2-17x+12=0 have a common root. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #573133 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=573133\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "find the value 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;\" > if the equations <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-2x%2Bp=0 ALIGN=MIDDLE  ALT=\"3x%5E2-2x%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-17x%2B12=0 ALIGN=MIDDLE  ALT=\"6x%5E2-17x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "have a common root \r<BR>\n" );
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document.write( "find roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-17x%2B12=0 ALIGN=MIDDLE  ALT=\"6x%5E2-17x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-9x-8x%2B12=0 ALIGN=MIDDLE  ALT=\"6x%5E2-9x-8x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E2-8x%29-%289x-12%29=0 ALIGN=MIDDLE  ALT=\"%286x%5E2-8x%29-%289x-12%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%283x-4%29-3%283x-4%29=0 ALIGN=MIDDLE  ALT=\"2x%283x-4%29-3%283x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-4%29%282x-3%29=0 ALIGN=MIDDLE  ALT=\"%283x-4%29%282x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....roots are\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-4%29=0 ALIGN=MIDDLE  ALT=\"%283x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=4 ALIGN=MIDDLE  ALT=\"3x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29=0 ALIGN=MIDDLE  ALT=\"%282x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=3 ALIGN=MIDDLE  ALT=\"2x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-2x%2Bp=0 ALIGN=MIDDLE  ALT=\"3x%5E2-2x%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4%2F3 ALIGN=MIDDLE  ALT=\"x=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is same root, then we have\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%284%2F3%29%5E2-2%284%2F3%29%2Bp=0 ALIGN=MIDDLE  ALT=\"3%284%2F3%29%5E2-2%284%2F3%29%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2816%2F9%29-2%284%2F3%29%2Bp=0 ALIGN=MIDDLE  ALT=\"3%2816%2F9%29-2%284%2F3%29%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%283%29%2816%2Fcross%289%293%29-%288%2F3%29%2Bp=0 ALIGN=MIDDLE  ALT=\"cross%283%29%2816%2Fcross%289%293%29-%288%2F3%29%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816%2F3%29-%288%2F3%29%2Bp=0 ALIGN=MIDDLE  ALT=\"%2816%2F3%29-%288%2F3%29%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3%2Bp=0 ALIGN=MIDDLE  ALT=\"8%2F3%2Bp=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=-%288%2F3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28p=-%288%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "check the roots using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-%288%2F3%29 ALIGN=MIDDLE  ALT=\"p=-%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-2x-%288%2F3%29=0 ALIGN=MIDDLE  ALT=\"3x%5E2-2x-%288%2F3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...both sides multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-6x-8=0 ALIGN=MIDDLE  ALT=\"9x%5E2-6x-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......factor\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-12x%2B6x-8=0 ALIGN=MIDDLE  ALT=\"9x%5E2-12x%2B6x-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%5E2-12x%29%2B%286x-8%29=0 ALIGN=MIDDLE  ALT=\"%289x%5E2-12x%29%2B%286x-8%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%283x-4%29%2B2%28x-4%29=0 ALIGN=MIDDLE  ALT=\"3x%283x-4%29%2B2%28x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%283x-4%29=0 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%283x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "roots:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%283x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=-2 ALIGN=MIDDLE  ALT=\"3x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2%2F3 ALIGN=MIDDLE  ALT=\"x=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-4%29=0 ALIGN=MIDDLE  ALT=\"%283x-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=4 ALIGN=MIDDLE  ALT=\"3x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...which is same as a root of a given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-17x%2B12=0 ALIGN=MIDDLE  ALT=\"6x%5E2-17x%2B12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "let's see it on a graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2Ccircle%284%2F3%2C0%2C.2%29%2Clocate%284%2F3%2C0%2Cp%284%2F3%2C0%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+6x%5E2-17x%2B12%2C+3x%5E2-2x-%288%2F3%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );