document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199414>Question 199414</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve for the discriminate and determine the number of solution and classify it for the equation:<BR>\n" );
document.write( "square root of 2x^2-4x-7sq root of 2-0<BR>\n" );
document.write( "can you help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149852 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=149852\">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( "I don't know what a 'discriminate' means with respect to a quadratic polynomial.  And you do not have an equation since there is no equals sign.  So I can't precisely answer the question you posed.\r<BR>\n" );
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document.write( "However, if you meant:\r<BR>\n" );
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document.write( "\"I need to calculate the <i>discriminant</i>, determine the number of solutions, and classify the solutions for the equation:  sqrt(2)x^2-4x-7*sqrt(2)<b>=</b>0\"\r<BR>\n" );
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document.write( "Then I can help.\r<BR>\n" );
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document.write( "Given a quadratic equation in standard form, namely:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ax^2 + bx + c = 0\">\r<BR>\n" );
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document.write( "You can calculate the discriminant, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta\">, by substituting the given coefficients into:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \Delta = b^2 - 4ac\">\r<BR>\n" );
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document.write( "Then you can classify the roots of the equation thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \Delta > 0 \ \ \Rightarrow\ \\"> Two real and unequal roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \Delta = 0 \ \ \Rightarrow\ \\"> One real root with a multiplicity of two.  That is to say that the trinomial is a perfect square and has two identical factors.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \Delta < 0 \ \ \Rightarrow\ \\"> A conjugate pair of complex roots of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a \pm bi\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE i\"> is the imaginary number defined by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE i^2 = -1\">\r<BR>\n" );
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document.write( "For your problem: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a = \sqrt{2}\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large b = -4\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c = -7\sqrt{2}\">, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \Delta = (-4)^2 - 4(\sqrt{2})(-7\sqrt{2})\">\r<BR>\n" );
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document.write( "You can do your own arithmetic and then evaluate according to the criteria listed.\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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