document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=695911>Question 695911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the product of the solutions of this equation. 3x^2 - 12x + 7 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854055 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53712)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "Find the product of the solutions of this equation. 3x^2 - 12x + 7 = 0.<BR>\n" );
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document.write( "This is a nice question, &nbsp;and it has a nice answer.\r<BR>\n" );
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document.write( "To get the product of the roots of this equation, &nbsp;you do not need to solve the equation <BR>\n" );
document.write( "and you do not need to find the roots explicitly, &nbsp;as the other tutor makes in his post.\r<BR>\n" );
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document.write( "Instead, &nbsp;use the &nbsp;Vieta's theorem.\r<BR>\n" );
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document.write( "It says that the product of the roots of a quadratic equation &nbsp;&nbsp;ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "is always &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fa ALIGN=MIDDLE  ALT=\"c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;&nbsp;or the constant term divided by the leading coefficient at &nbsp;x^2.\r<BR>\n" );
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document.write( "In your case, &nbsp;the product of the roots is  &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F3 ALIGN=MIDDLE  ALT=\"7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  &nbsp;&nbsp;so you get the answer instantly, &nbsp;without making long calculations.\r<BR>\n" );
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document.write( "The &nbsp;Vieta's theorem works for real roots and for complex roots: &nbsp;in other words, &nbsp;it works for any quadratic equation.\r<BR>\n" );
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document.write( "It is &nbsp;UNIVERSAL.\r<BR>\n" );
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document.write( "This problem is specially given to you to check if you are familiar with the &nbsp;Vieta's theorem,\r<BR>\n" );
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document.write( "and if you are not familiar with it, &nbsp;it is a good chance to learn it and to see how perfectly it works.\r<BR>\n" );
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document.write( "It is also a good question for an interview, since it allows to learn momentarily,<BR>\n" );
document.write( "if a person knows Algebra and generally a school Math uniformly.<BR>\n" );
document.write( "How a person answers this question, it demonstrates/reflects the person's mathematical culture.\r<BR>\n" );
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