document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887630>Question 887630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of k that makes the sum of the roots of 3x^2+18=(3k+2)x equal to 6. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536773 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=536773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sum of the roots are equal to -b/a<BR>\n" );
document.write( "the product of the roots are equal to c/a<BR>\n" );
document.write( "the standard form of the quadratic equation is ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "your equation is:<BR>\n" );
document.write( "3x^2 + 18 = (3k+2)x\r<BR>\n" );
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document.write( "subtract (3k+2)x from both sides of the equation to get:<BR>\n" );
document.write( "3x^2 - (3k+2)x + 18 = 0\r<BR>\n" );
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document.write( "this equation is now in standard form of ax^2 + bx + c where:<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = -(3k+2)<BR>\n" );
document.write( "c = 18\r<BR>\n" );
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document.write( "sum of the roots are -b/a which becomes (3k+2)/3.\r<BR>\n" );
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document.write( "since sum of the roots is equal to 6, this means that (3k+2)/3 = 6.\r<BR>\n" );
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document.write( "multiply both sides of this equation by 3 to get:<BR>\n" );
document.write( "3k+2 = 18\r<BR>\n" );
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document.write( "subtract 2 from both sides of this equation to get:<BR>\n" );
document.write( "3k = 16\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get;<BR>\n" );
document.write( "k = 16/3\r<BR>\n" );
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document.write( "that should be the value of k.\r<BR>\n" );
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document.write( "let's see if that works.\r<BR>\n" );
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document.write( "when k = 16/3, 3k+2 = 3*16/3 + 2 = 18.\r<BR>\n" );
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document.write( "your equation of 3x^2 + 18 = (3k+2)x becomes:<BR>\n" );
document.write( "3x^2 + 18 = 18x\r<BR>\n" );
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document.write( "subtract 18x from both sides of this equation to get:<BR>\n" );
document.write( "3x^2 - 18x + 18 = 0\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get:<BR>\n" );
document.write( "x^2 - 6x + 6 = 0\r<BR>\n" );
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document.write( "we can use the formula of sum of the roots = -b/a to get 6/1 = 6.\r<BR>\n" );
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document.write( "let's find the roots to see if the formula gave us the right answer.\r<BR>\n" );
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document.write( "the roots of this equation are:\r<BR>\n" );
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document.write( "x = (6 - sqrt(12))/ 2 and x = (6 + sqrt(12)) / 2\r<BR>\n" );
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document.write( "the sum of the roots are (6 - sqrt(12)) / 2 + (6 + sqrt(12)) / 2\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "sum = (6 - sqrt(12) + 6 + sqrt(12)) / 2\r<BR>\n" );
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document.write( "simplify this to get sum = 12 / 2 because the + sqrt(12) and the - sqrt(12) cancel out.\r<BR>\n" );
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document.write( "simplify further to get sum = 6.\r<BR>\n" );
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document.write( "the formula for sum of roots = -b/a works and the solution is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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