document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127200>Question 127200</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k???? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93191 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=93191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k????<BR>\n" );
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document.write( "If 5+2sqrt(3)i is a root, so is 5-2sqrt(3)i.<BR>\n" );
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document.write( "Then the following product is a factor of the given polynomial:<BR>\n" );
document.write( "(x-(5+2sqrt(3)i)(x-(5-2sqrt(3)i)\r<BR>\n" );
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document.write( "= ((x-5)-2sqrt(3)i)((x-5)+2sqrt(3)i)<BR>\n" );
document.write( "Comment: Notice that the factors are in the form (a-b)(a+b).<BR>\n" );
document.write( "So the product is a^2-b^2<BR>\n" );
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document.write( "= (x-5)^2 -(2sqr(3)i)^2\r<BR>\n" );
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document.write( "= x^2-10x+25+12\r<BR>\n" );
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document.write( "= x^2-12x+37\r<BR>\n" );
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document.write( "Comparing that to the original polynominal you see that<BR>\n" );
document.write( "k = 37<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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