document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=569266>Question 569266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find a quadratic equation if you are only given the solution?  Is it possible to have different equadratic equations with the same solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367329 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=367329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can find the quadratic equation given the roots. Suppose the roots are p and q (quadratics will only have two roots). Then x-p and x-q are factors of the quadratic, and the quadratic will look like\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x-p)(x-q) = x^2 - (p+q)x + pq\">\r<BR>\n" );
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document.write( "There are infinitely many quadratics that satisfy, but they will all differ by a constant factor, i.e.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE C(x^2 - (p+q)x + pq)\">\r<BR>\n" );
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document.write( "where C is any constant not equal to 0. </SPAN>\n" );
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