document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=329177>Question 329177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Create your own quadratic equation that cannot be solved by factoring, but can be solved using the quadratic formula. Identify the values of a, b, and c, and find the solutions using the quadratic formula. Show all work to receive credit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235881 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The way to attack this one is to use the idea that if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \alpha\"> is a zero of of a polynomial function, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ -\ \alpha\"> must be a factor of the polynomial.  Further we know that irrational roots of polynomial equations always come in conjugate pairs.\r<BR>\n" );
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document.write( "So, let's say that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \rho\ +\ \sqrt{\sigma}\">\r<BR>\n" );
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document.write( "is a root of our quadratic equation.  From that we can determine two things.  First:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \rho\ -\ \sqrt{\sigma}\">\r<BR>\n" );
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document.write( "is the other zero of the function and the factors of the quadratic trinomial are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ (\rho\ +\ \sqrt{\sigma})\right)\left(x\ -\ (\rho\ -\ \sqrt{\sigma})\right)\">\r<BR>\n" );
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document.write( "Which, in order to be a quadratic equation in standard form, must be multiplied using FOIL and set equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 2\rho x\ +\ \rho^2\ -\ \sigma\ =\ 0\">\r<BR>\n" );
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document.write( "Now you have a quadratic equation in standard form, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large ax^2\ +\ bx\ +\ c\ =\ 0\"> where\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ =\ 1\ \ \">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b\ =\ -2\rho\ \ \">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE c\ =\ \rho^2\ -\ \sigma\">\r<BR>\n" );
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document.write( "You can leave your answer like that, or pick a couple of numbers to substitute for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \rho\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sigma\">.  Pick any numbers you like as long as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sigma\"> is NOT a perfect square.  (If you pick a perfect square for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sigma\">, then your quadratic will turn out to be factorable)\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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