document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=507247>Question 507247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following polynomials is prime over the set of rational numbers?\r<BR>\n" );
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document.write( "a.x^2-13x-36<BR>\n" );
document.write( "b.x^2-5x-36<BR>\n" );
document.write( "c.x^2+15x+36<BR>\n" );
document.write( "d.x^2+20x+36 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340377 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=340377\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which of the following polynomials is prime over the set of rational numbers?<BR>\n" );
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document.write( "x = (-b/(2a)] +- [sqrt(b^2-4ac)]/(2a),<BR>\n" );
document.write( "Check the discriminant (b^2-4ac) for each of the quadratics.<BR>\n" );
document.write( "If b^2-4ac is not a perfect square the quadratic is prime over the rationals.\r<BR>\n" );
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document.write( "a.x^2-13x-36<BR>\n" );
document.write( "13^2-4*36 = 25 <BR>\n" );
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document.write( "b.x^2-5x-36<BR>\n" );
document.write( "5^2 - 4*-36 = 169<BR>\n" );
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document.write( "c.x^2+15x+36<BR>\n" );
document.write( "15^2 -4*36 = 225 - 144 = 81<BR>\n" );
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document.write( "d.x^2+20x+36<BR>\n" );
document.write( "20^2-4*36 = 16<BR>\n" );
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document.write( "Conclusion: None of those quadratics is prime over the rationals. \r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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