document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464016>Question 464016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.<BR>\n" );
document.write( "x^2 = 6x + 2 <BR>\n" );
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document.write( "a) Two different irrational solutions<BR>\n" );
document.write( "b) Exactly one rational solution<BR>\n" );
document.write( "c) Two different rational solutions<BR>\n" );
document.write( "d) Two different imaginary solutions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317839 by </B><A HREF=/tutors/aboutme.mpl?userid=algebrahouse.com><B>algebrahouse.com(1659)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=algebrahouse.com><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=algebrahouse.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b² - 4ac is the discriminant\r<BR>\n" );
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document.write( "If b² - 4ac = 0, then there is one real number solution<BR>\n" );
document.write( "If b² - 4ac < 0, then there are two imaginary number solutions<BR>\n" );
document.write( "If b² - 4ac > 0, then there are two real number solutions\r<BR>\n" );
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document.write( "x² = 6x + 2<BR>\n" );
document.write( "x² - 6x - 2 = 0 {subtracted 6x and 2 from both sides}<BR>\n" );
document.write( "a = 1, b = -6, c = -2 \r<BR>\n" );
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document.write( "b² - 4ac {the discriminant}<BR>\n" );
document.write( "= (-6)² - 4(1)(-2) {substituted into the discriminant}<BR>\n" );
document.write( "= 36 + 8 {simplified}<BR>\n" );
document.write( "= 44 {added}<BR>\n" );
document.write( "44 > 0\r<BR>\n" );
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document.write( "There are two different real number solutions ,<BR>\n" );
document.write( "however &#8730;44 is irrational, therefore there are<BR>\n" );
document.write( "A.) Two different irrational solutions<BR>\n" );
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