document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=871953>Question 871953</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the two roots of the equation: X^2+X-3=0 are M and N:\r<BR>\n" );
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document.write( "a. Form the equation that has the roots 1/M, 1/M.<BR>\n" );
document.write( "b. Form the equation that has the roots M^2, N^2. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #525953 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=525953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "If the two roots of the equation: x^2+x-3=0 are m and n, then\r<BR>\n" );
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document.write( "(x-m)(x-n) = x^2+x-3<BR>\n" );
document.write( "x^2-xm-xn+mn = x^2+x-3<BR>\n" );
document.write( "x^2-(m+n)x+mn = x^2+x-3\r<BR>\n" );
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document.write( "Equate coefficients to get\r<BR>\n" );
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document.write( "-(m+n) = 1 which leads to m+n = -1<BR>\n" );
document.write( "mn = -3\r<BR>\n" );
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document.write( "Now square both sides and isolate m^2 + n^2\r<BR>\n" );
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document.write( "m+n = -1<BR>\n" );
document.write( "(m+n)^2 = (-1)^2<BR>\n" );
document.write( "(m+n)^2 = 1<BR>\n" );
document.write( "m^2 + 2mn + n^2 = 1<BR>\n" );
document.write( "m^2 + 2(-3) + n^2 = 1 ... plug in mn = -3<BR>\n" );
document.write( "m^2 - 6 + n^2 = 1<BR>\n" );
document.write( "m^2 + n^2 = 1 + 6<BR>\n" );
document.write( "m^2 + n^2 = 7\r<BR>\n" );
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document.write( "a) If the roots are 1/m and 1/n, then...\r<BR>\n" );
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document.write( "(x - 1/m)(x - 1/n)<BR>\n" );
document.write( "x^2 - x/m - x/n + 1/mn<BR>\n" );
document.write( "x^2 - (1/m + 1/n)x + 1/mn<BR>\n" );
document.write( "x^2 - (n/mn + m/mn)x + 1/mn<BR>\n" );
document.write( "x^2 - ((n + m)/mn)x + 1/mn<BR>\n" );
document.write( "x^2 - ((m + n)/mn)x + 1/mn<BR>\n" );
document.write( "x^2 - ((-1)/mn)x + 1/mn<BR>\n" );
document.write( "x^2 - ((-1)/(-3))x + 1/(-3)<BR>\n" );
document.write( "x^2 - (1/3)x - 1/3\r<BR>\n" );
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document.write( "If the roots are 1/m and 1/n, then the polynomial is x^2 - (1/3)x - 1/3\r<BR>\n" );
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document.write( "b) If the roots are m^2 and n^2, then \r<BR>\n" );
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document.write( "(x - m^2)(x - n^2)<BR>\n" );
document.write( "x^2 - xn^2 - xm^2 + m^2n^2<BR>\n" );
document.write( "x^2 - (n^2 + m^2)x + (mn)^2<BR>\n" );
document.write( "x^2 - (m^2 + n^2)x + (mn)^2<BR>\n" );
document.write( "x^2 - (7)x + (-3)^2<BR>\n" );
document.write( "x^2 - 7x + 9\r<BR>\n" );
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document.write( "If the roots are m^2 and n^2, then the polynomial is x^2 - 7x + 9<BR>\n" );
document.write( " </SPAN>\n" );
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