document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697487>Question 697487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what types of roots does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B10=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B10=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > have?\r<BR>\n" );
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document.write( "my work:\r<BR>\n" );
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document.write( "a=1<BR>\n" );
document.write( "b=-6<BR>\n" );
document.write( "c=10<BR>\n" );
document.write( "4ac=40\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B+or+-+sqrt%2836-40%29%29%2F2 ALIGN=MIDDLE  ALT=\"%286%2B+or+-+sqrt%2836-40%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B+or+-+sqrt%28-4%29%29%2F2 ALIGN=MIDDLE  ALT=\"%286%2B+or+-+sqrt%28-4%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B+or+-+i+sqrt%284%29%29%2F2 ALIGN=MIDDLE  ALT=\"%286%2B+or+-+i+sqrt%284%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >       \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29 ALIGN=MIDDLE  ALT=\"sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B+or+-+2i%29%2F2 ALIGN=MIDDLE  ALT=\"%286%2B+or+-+2i%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "cancel the 2's out and simplify the 6. final answer: \r<BR>\n" );
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document.write( "3+ or - i\r<BR>\n" );
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document.write( "I know I found the roots. Because of the i does this mean the roots are irrational? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430065 by </B><A HREF=/tutors/aboutme.mpl?userid=Positive_EV><B>Positive_EV(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Positive_EV><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=Positive_EV><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=430065\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can use the discriminant to determine the nature of the roots: the discriminant is the part of the quadratic formula under the square root sign; that is, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4%2Aa%2Ac ALIGN=MIDDLE  ALT=\"b%5E2+-+4%2Aa%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If the discriminant is positive, there are two real roots. If it is zero, there is a single double root. If it is negative, there are two imaginary roots.<br>\r<BR>\n" );
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document.write( "Here, a = 1, b = -6 c = 10, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4%2Aa%2Ac+=+%28-6%29%5E2+-+4%2A%281%29%2A%28-10%29+=+-4 ALIGN=MIDDLE  ALT=\"b%5E2+-+4%2Aa%2Ac+=+%28-6%29%5E2+-+4%2A%281%29%2A%28-10%29+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br>\r<BR>\n" );
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document.write( "The discriminant is negative, so the equation has two imaginary roots. </SPAN>\n" );
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