document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=384398>Question 384398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can you have one solution in something that is quadratic? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #272130 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=272130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When b^2 - 4ac is equal to 0, you will have 1 solution.\r<BR>\n" );
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document.write( "The standard form of the quadratic equation is:\r<BR>\n" );
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document.write( "ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "a is the coefficient of the x^2 term.<BR>\n" );
document.write( "b is the coefficient of the x term.<BR>\n" );
document.write( "c is the constant term.\r<BR>\n" );
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document.write( "To find the roots of this equation, you can use the quadratic formula.\r<BR>\n" );
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document.write( "the quadratic formula is:\r<BR>\n" );
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document.write( "x = -b +/- sqrt(b^2-4ac)\r\n" );
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document.write( "             2a\r\n" );
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document.write( "If b^2 - 4ac is equal to 0, then you have +/- 0 in the numerator and there is only one solution to the problem.\r<BR>\n" );
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document.write( "We can construct an example to show you what I mean.\r<BR>\n" );
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document.write( "To construct this example, let's pick a b term at random.\r<BR>\n" );
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document.write( "Let's say b is equal to 6.\r<BR>\n" );
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document.write( "That makes b^2 = 36\r<BR>\n" );
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document.write( "Divide 36 by 4 to get 9.\r<BR>\n" );
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document.write( "We need to get a * c to be equal to 9.\r<BR>\n" );
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document.write( "a * c will be equal to 9 when a = 1 and c = 9\r<BR>\n" );
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document.write( "We have:\r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = 6<BR>\n" );
document.write( "c = 9\r<BR>\n" );
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document.write( "b^2 - 4ac becomes 36 - (4*1*9) which becomes 36 - 36 which becomes 0.\r<BR>\n" );
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document.write( "Our quadratic equation should have one solution only.\r<BR>\n" );
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document.write( "The standard form of the quadratic equation is ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "Since a = 1, b = 6 and c = 9, this equation becomes:\r<BR>\n" );
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document.write( "x^2 + 6x + 9 = 0\r<BR>\n" );
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document.write( "We will now graph this equation as shown below:\r<BR>\n" );
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document.write( "You can see from the graph that the graph of the quadratic equation touches the x-axis at the point x = -3 and only at that point.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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