document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=838938>Question 838938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one of the roots of 3x^2+p=5x, is 2.determine the value of p and the other root </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505431 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if one of the roots of the equation is x = 2, then f(2) must be equal to 0.\r<BR>\n" );
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document.write( "start with 3x^2 + p = 5x<BR>\n" );
document.write( "subtract 5x from both sides of this equation to get:<BR>\n" );
document.write( "3x^2 - 5x + p = 0<BR>\n" );
document.write( "replace x with 2 in the equation to get:<BR>\n" );
document.write( "3(2)^2 - 5(2) + p = 0<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "12 - 10 + p = 0<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "2 + p = 0<BR>\n" );
document.write( "solve for p to get:<BR>\n" );
document.write( "p = -2\r<BR>\n" );
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document.write( "your expression becomes:<BR>\n" );
document.write( "3x^2 - 5x - 2 = 0\r<BR>\n" );
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document.write( "factor this equation to get:<BR>\n" );
document.write( "(3x + 1) * (x-2) = 0<BR>\n" );
document.write( "your factors will be:<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "x = -1/3\r<BR>\n" );
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document.write( "to confirm, replace x with -1/3 in the original equation to see if it holds true.\r<BR>\n" );
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document.write( "original equation is:<BR>\n" );
document.write( "3x^2 + p = 5x<BR>\n" );
document.write( "replace p with -2 to get:<BR>\n" );
document.write( "3x^2 - 2 = 5x<BR>\n" );
document.write( "replace x with (-1/3) to get:<BR>\n" );
document.write( "3(-1/3)^2 - 2 = 5*(-1/3)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "3 * 1/9 - 2 = -5/3<BR>\n" );
document.write( "convert everything to a common denominator of 9 to get:<BR>\n" );
document.write( "3/9 - 18/9 = -15/9<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "-15/9 = -15/9<BR>\n" );
document.write( "this confirms that -1/3 is a root of the equation.\r<BR>\n" );
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document.write( "you can do the same with x = 2 to confirm it is also a solution to the equation.<BR>\n" );
document.write( "original equation is:<BR>\n" );
document.write( "3x^2 + p = 5x<BR>\n" );
document.write( "replace p with -2 to get:<BR>\n" );
document.write( "3x^2 - 2 = 5x<BR>\n" );
document.write( "replace x with 2 to get:<BR>\n" );
document.write( "3(2)^2 - 2 = 5*(2)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "12 - 2 = 10<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "10 = 10<BR>\n" );
document.write( "this confirms that 2 is a root of the equation.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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