document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=244371>Question 244371</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello there wonderful tutor, i am in need of your fine assistance, if you would be so kind! this problem has been rattling my brain---please save me!!!          here it is.....<BR>\n" );
document.write( "A polynomial equation for the variable x and of the smallest degree with rational coefficients has one root of: sqrt(3)+ sqrt(2) all over sqrt(3)-sqrt(2)... and a second root of: sqrt(11)+sqrt(10) all over sqrt(11)-sqrt(10).....  If the coefficient of the x term in the polynomial equation is -52, find the coefficient of the x^2 term.<BR>\n" );
document.write( "(i just added the colons and dot dot dots for organization) <BR>\n" );
document.write( "ok, PLEASE help!!!!!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178762 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=178762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"one root of: sqrt(3)+ sqrt(2) all over sqrt(3)-sqrt(2)\"<BR>\n" );
document.write( "___ multiplying numerator and denominator by [sqrt(3)+ sqrt(2)] ___ 5 + 2 sqrt(6)<BR>\n" );
document.write( "___ conjugate root ___ 5 - 2 sqrt(6)<BR>\n" );
document.write( "___ resulting factor [(x - R1)(x - C1)] ___ x^2 - 10x + 1\r<BR>\n" );
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document.write( "\"second root of: sqrt(11)+sqrt(10) all over sqrt(11)-sqrt(10)\"<BR>\n" );
document.write( "___ multiplying numerator and denominator by [sqrt(11)+ sqrt(10)] ___ 21 + 2 sqrt(110)<BR>\n" );
document.write( "___ conjugate root ___ 21 - 2 sqrt(110)<BR>\n" );
document.write( "___ resulting factor [(x - R2)(x - C2)] ___ x^2 - 42x + 1\r<BR>\n" );
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document.write( "multiplying the factors ___ x^4 - 52x^3 + 422x^2 - 52x + 1 </SPAN>\n" );
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