document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182396>Question 182396</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0078279992/algebrahomeworkh>Algebra2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Complete parts a-c for each quadratic equation<BR>\n" );
document.write( "a) find the value of the discriminant<BR>\n" );
document.write( "b) describe the number and type of roots<BR>\n" );
document.write( "c) find the exact solutions by using the Quadratic Formula \r<BR>\n" );
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document.write( "16) x^2-2x+5=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136889 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=136889\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math x^2-2x+5=0\">\r<BR>\n" );
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document.write( "Quadratic formula:\r<BR>\n" );
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document.write( "Given: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math ax^2+bx+c=0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math x_{1,2} = \frac {-b \pm sqrt{b^2 - 4ac}}{2a}\">\r<BR>\n" );
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document.write( "The discriminant, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta\"> is the value of the expression under the radical in the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \Delta = b^2 - 4ac\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta > 0 \ \ \Rightarrow\ \ \"> Roots are real and unequal.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta = 0 \ \ \Rightarrow\ \ \"> Roots are real and equal.  Also expressed as a single root with a multiplicity of 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \Delta < 0 \ \ \Rightarrow\ \ \"> Roots are a conjugate pair of complex numbers of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a \pm bi\"> where <i>i</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:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math a = 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math b = -2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math c = 5\">\r<BR>\n" );
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document.write( "Hence \r<BR>\n" );
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document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math \Delta = (-2)^2 - 4(1)(5) = -16 < 0\">\r<BR>\n" );
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document.write( "b) Therefore, the roots are a conjugate pair of complex numbers.\r<BR>\n" );
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document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math x_{1,2} = \frac {-(-2) \pm sqrt{(-2)^2 - 4(1)(5)}}{2(1)} = \frac {2 \pm sqrt{-16}}{2} = \frac {2 \pm 4i}{2} = 1 \pm 2i\">\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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