document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045791>Question 1045791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having the most difficult time figuring out how to format this into a polynomial. I know the highest exponent degree must be at 4, and that it also must include x^2 but that is all I can figure out. Any help would be much appreciated.\r<BR>\n" );
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document.write( "Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; Zeros -5+5i; 1 multiplicity 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #661283 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=661283\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation is degree 4.<BR>\n" );
document.write( "therefore you should have 4 roots.<BR>\n" );
document.write( "the highest exponent will be 4.\r<BR>\n" );
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document.write( "let's look at what you have:\r<BR>\n" );
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document.write( "you are asked to Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; Zeros -5+5i; 1 multiplicity 2\r<BR>\n" );
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document.write( "your roots are, or should have been given as:\r<BR>\n" );
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document.write( "x = 5 plus or minus 5i,<BR>\n" );
document.write( "x = 1 with a multiplicity of 2.\r<BR>\n" );
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document.write( "complex roots always come in pairs.\r<BR>\n" );
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document.write( "if a + bi is a root, then a - bi is also a root.\r<BR>\n" );
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document.write( "to find the factors, your set x equal to the root and then set the equation equal to 0.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "x = 1 is set to 0 by doing the following:<BR>\n" );
document.write( "subtract 1 from both sides of the equation to get x - 1 = 0<BR>\n" );
document.write( "x - 1 is a factor.\r<BR>\n" );
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document.write( "they told you the root has a multiplicity of 2, therefore 2 of your factors are (x-1) * (x-1) which can also be written as (x-1)^2.\r<BR>\n" );
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document.write( "your complex roots come in pairs.\r<BR>\n" );
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document.write( "they should be 5 + 5i and 5 - 51.\r<BR>\n" );
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document.write( "set x = 5 + 5i<BR>\n" );
document.write( "subtract 5 + 5i from both sides of the equation to get:<BR>\n" );
document.write( "x - 5 - 5i = 0<BR>\n" );
document.write( "that's one of the complex factors.\r<BR>\n" );
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document.write( "set x = 5 - 5i<BR>\n" );
document.write( "subtract 5 from both sides of the equation and add 5i to both sides of the equation to get:<BR>\n" );
document.write( "x - 5 + 5i = 0<BR>\n" );
document.write( "that's the other of the complex factors.\r<BR>\n" );
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document.write( "your factors are (x-1)^2 * (x - 5 - 5i) * (x - 5 + 5i)\r<BR>\n" );
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document.write( "your equation will be:\r<BR>\n" );
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document.write( "(x-1)^2 * (x - 5 - 5i) * (x - 5 + 5i) = 0\r<BR>\n" );
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document.write( "multiply these factors out to get your equation.\r<BR>\n" );
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document.write( "(x - 5 - 5i) * (x = 5 + 5i) results in x^2 - 10x + 50\r<BR>\n" );
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document.write( "(x-1)^2 results in x^2 - 2x + 1\r<BR>\n" );
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document.write( "your equation would be:\r<BR>\n" );
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document.write( "(x^2 - 10x + 50) * (x^2 - 2x + 1) = 0\r<BR>\n" );
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document.write( "the result of that would be:\r<BR>\n" );
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document.write( "x^4 - 12x^3 + 71x^2 - 110x + 50 = 0\r<BR>\n" );
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document.write( "the general equation is y = x^4 - 12x^3 + 71x^2 -110x + 50.\r<BR>\n" );
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document.write( "to factor that equation, you set y = 0 to get what we had before as:\r<BR>\n" );
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document.write( "x^4 - 12x^3 + 71x^2 - 110x + 50 = 0\r<BR>\n" );
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document.write( "now it's in standard form for factoring.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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