document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553408>Question 553408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Question is:<BR>\n" );
document.write( "Given a Quadratic equation with rational coefficients with a root of 6+5i<BR>\n" );
document.write( "a) What is another root to this equation? <BR>\n" );
document.write( "b) What are the factors of the equation? <BR>\n" );
document.write( "c) What is the quadratic equation with the given root?<BR>\n" );
document.write( "d) What is the representative function? <BR>\n" );
document.write( "I know this is long but i tried and my teacher took up my references to grade them, and I don't remember any of the rules. I think answer a is 6-5i. Can you please help? This is a very important grade and I have no room for mistakes. Thank You for any help :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360822 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=360822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) What is another root to this equation?\r<BR>\n" );
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document.write( "If a+bi is one root, then the conjugate a-bi is another root\r<BR>\n" );
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document.write( "So 6 - 5i is another root\r<BR>\n" );
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document.write( "b) What are the factors of the equation?\r<BR>\n" );
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document.write( "If p and q are roots, then x-p and x-q are factors\r<BR>\n" );
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document.write( "So if 6+5i and 6-5i are roots, then x-(6+5i) and x-(6-5i) are factors\r<BR>\n" );
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document.write( "They can be simplified to x-6-5i and x-6+5i\r<BR>\n" );
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document.write( "c) What is the quadratic equation with the given root?\r<BR>\n" );
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document.write( "Multiply the factors to get \r<BR>\n" );
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document.write( "(x-6-5i)(x-6+5i)\r<BR>\n" );
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document.write( "((x-6)-5i)((x-6)+5i)\r<BR>\n" );
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document.write( "(x-6)^2-(5i)^2 ... Note: I'm using the difference of squares formula here\r<BR>\n" );
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document.write( "(x-6)^2-25i^2\r<BR>\n" );
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document.write( "(x-6)^2-25(-1)\r<BR>\n" );
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document.write( "(x-6)^2+25\r<BR>\n" );
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document.write( "x^2-12x+36+25\r<BR>\n" );
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document.write( "x^2-12x+61\r<BR>\n" );
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document.write( "So the quadratic equation with the given root is x^2-12x+61 = 0\r<BR>\n" );
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document.write( "d) What is the representative function? \r<BR>\n" );
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document.write( "The function is f(x) = x^2-12x+61\r<BR>\n" );
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document.write( "All we're doing here is replacing the =0 part with f(x) = ...\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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