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 #525817 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=525817\">put this solution on YOUR website!</A><BR><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( "sum of roots = -b/a  in equation ax^2+bx +c =0\r<BR>\n" );
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document.write( "product of roots = c/a\r<BR>\n" );
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document.write( "Therefore in x^2+x-3 =0<BR>\n" );
document.write( "M+N = =-1 <BR>\n" );
document.write( "MN = -3\r<BR>\n" );
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document.write( "The roots of the required equation are 1/M & 1/N\r<BR>\n" );
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document.write( "First we find the value of 1/M + 1/N and 1/MN and substitute (M+N) and MN\r<BR>\n" );
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document.write( "1/M + 1/N = (M+N)/MN = -1/-3 = 1/3\r<BR>\n" );
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document.write( "1/M * 1/N = 1/MN = 1/-3= -1/3\r<BR>\n" );
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document.write( "The required equation is <BR>\n" );
document.write( "x^2-(sum of roots)x + ( product of roots =0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%281%2F3%29x+%2B+%28-1%2F3%29=0 ALIGN=MIDDLE  ALT=\"x%5E2-%281%2F3%29x+%2B+%28-1%2F3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "mmultiply equation by 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-x-1=0 ALIGN=MIDDLE  ALT=\"3x%5E2-x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "M^ N^2 are the roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5E2%2BN%5E2=+%28M%2BN%29%5E2-+2MN+=++%281%2F3%29%5E2+-+%28-3%29=+1%2F9+%2B3+=+13%2F9 ALIGN=MIDDLE  ALT=\"M%5E2%2BN%5E2=+%28M%2BN%29%5E2-+2MN+=++%281%2F3%29%5E2+-+%28-3%29=+1%2F9+%2B3+=+13%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M%5E2N%5E2+=+%28MN%29%5E2+=+%28-3%29%5E2+=+9 ALIGN=MIDDLE  ALT=\"M%5E2N%5E2+=+%28MN%29%5E2+=+%28-3%29%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "frame the equation as done above\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-+%2813%2F9%29x%2B9+=0 ALIGN=MIDDLE  ALT=\"x%5E2-+%2813%2F9%29x%2B9+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "multiply by 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-13x%2B81+=0 ALIGN=MIDDLE  ALT=\"9x%5E2-13x%2B81+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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