document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=407617>Question 407617</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a, b, and c in a quadratic equation are all integers, is the product always rational? explain </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #287305 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=287305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The product of the roots is always rational. Suppose that the quadratic is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I'll divide both sides by a to obtain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If we assume the roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-r%5B1%5D%29%28x-r%5B2%5D%29+=+x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29x+%2B+r%5B1%5Dr%5B2%5D ALIGN=MIDDLE  ALT=\"%28x-r%5B1%5D%29%28x-r%5B2%5D%29+=+x%5E2+-+%28r%5B1%5D+%2B+r%5B2%5D%29x+%2B+r%5B1%5Dr%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5Dr%5B2%5D+=+c%2Fa ALIGN=MIDDLE  ALT=\"r%5B1%5Dr%5B2%5D+=+c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D+%2B+r%5B2%5D+=+-b%2Fa ALIGN=MIDDLE  ALT=\"r%5B1%5D+%2B+r%5B2%5D+=+-b%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >. These are sometimes called Vieta's formulas. </SPAN>\n" );
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