document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463547>Question 463547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 7x^2 + 4x = 3 , which of the following is (are) true?\r<BR>\n" );
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document.write( "I. The sum of the solutions is positive.<BR>\n" );
document.write( "II. The product of the solutions is negative.<BR>\n" );
document.write( "III. Both solutions are integers.\r<BR>\n" );
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document.write( "a) I only<BR>\n" );
document.write( "b) II only<BR>\n" );
document.write( "c) III only<BR>\n" );
document.write( "d) I and II only<BR>\n" );
document.write( "e) II and III only </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317629 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 7x^2 + 4x - 3 = 0\">\r<BR>\n" );
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document.write( "Know Vieta's formulas, which say that if you have a polynomial\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 = 0\">\r<BR>\n" );
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document.write( "Then the sum of the roots is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\frac{a_{n-1}}{a_n}\"> and the product of the roots is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{a_0}{a_n}\"> (plus, a whole bunch of other identities can be derived but we won't need them here).\r<BR>\n" );
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document.write( "Here, the sum of the solutions is -4/7, which is not positive, so I is not true. The product of the solutions is (-3)/7, negative, so II is true. We automatically know III cannot be true since if both solutions were integers, their sum would be an integer, but we already know I is not true. Hence, only II is true; answer is B.\r<BR>\n" );
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document.write( "For certain math problems, it can help to find a slick, fast solution. Here we were able to do it without even finding the roots of the quadratic. </SPAN>\n" );
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