document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207562>Question 1207562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the roots of the equation ax^2 + bx + c is equals to zero are alpha and beta find the equation whose roots are Alpha square and beta square </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845497 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=845497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the roots of the equation ax^2 + bx + c is equals to zero are alpha and beta find the equation whose roots are Alpha square and beta square\r<BR>\n" );
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document.write( "Instead of alpha and beta i will use p& q respectively\r<BR>\n" );
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document.write( "ax^2 + bx + c =0\r<BR>\n" );
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document.write( "p+q = -b/a  and pq = c/a\r<BR>\n" );
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document.write( "(p+q)^2 = b^2/a^2\r<BR>\n" );
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document.write( "we have to find equation with roots p^2  and q^2\r<BR>\n" );
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document.write( "p^2+q^2 = (p+q)^2-2pq (from identity)\r<BR>\n" );
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document.write( "substitute (p+q)^2 and pq\r<BR>\n" );
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document.write( "sum of roots\r<BR>\n" );
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document.write( "p^2+q^2 = b^2/a^2-2(c/a)  \r<BR>\n" );
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document.write( "product of roots\r<BR>\n" );
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document.write( "p2q^2= (pq)^2 = c^2/a^2  \r<BR>\n" );
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document.write( "The general form of a quadratic equation is x^2-(sum of roots)x+(product of roots)=0\r<BR>\n" );
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document.write( "x^2- (b^2/a^2-2(c/a)  )x +c^2/a^2=0\r<BR>\n" );
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document.write( "x^2- ((b^2-2ac)/a^2)  )x +c^2/a^2=0\r<BR>\n" );
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document.write( "multiply by a^2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2x%5E2+-%28b%5E2-2ac%29x+%2Bc%5E2=0 ALIGN=MIDDLE  ALT=\"a%5E2x%5E2+-%28b%5E2-2ac%29x+%2Bc%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a\r<BR>\n" );
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document.write( " </SPAN>\n" );
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