document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=541963>Question 541963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question from my book says that \"the radicand of the quadratic formula, b^2 - 4ac, can be used to determine whether <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+bx+%2B+c+=+a ALIGN=MIDDLE  ALT=\"+ax%5E2+%2B+bx+%2B+c+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > has solutions that are rational, irrational, or not real numbers.\" I haven't been able to solve the problem on this website because it's saying that the first coefficient is zero. It's also asking me to explain how this works. And if it possible to determine the kinds of answers that one will obtain to a quadratic equation without actually solving the equation. I would greatly appreciate any help I can get. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354362 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=354362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">Well, if the first coefficient is zero, then you would not have a quadratic equation, but a linear equation, ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bx%2Bc=a ALIGN=MIDDLE  ALT=\"bx%2Bc=a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Now, there are specific rules for using the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2-4ac%29 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2-4ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "a.) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2-4ac%29%3E0 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2-4ac%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will have 2 real solutions.<br>\r<BR>\n" );
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document.write( "b.) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2-4ac%29=0 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2-4ac%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will have 1 real solution.<br>\r<BR>\n" );
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document.write( "c.) If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28b%5E2-4ac%29%3C0 ALIGN=MIDDLE  ALT=\"sqrt%28b%5E2-4ac%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will have 2 imaginary solutions.<br>\r<BR>\n" );
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document.write( "Those are the only possible scenarios you can have with a quadratic equation.<br>\r<BR>\n" );
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document.write( "In part c, you will end up with a negative number under the radical, thus the reason for having only imaginary solutions.<br>\r<BR>\n" );
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document.write( "You would not know whether your solutions in part a would be rational or irrational until you simplified the radical.<br>\r<BR>\n" );
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document.write( "There is a lot more to using the quadratic formula, but I hope that this is a good start.<br>\r<BR>\n" );
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document.write( "There are many resources available online for learning more about the quadratic formula.<br>\r<BR>\n" );
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document.write( "I hope this helps!<br> </SPAN>\n" );
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