document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59260>Question 59260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Would someone be able to help me through a couple of these so I can get a better grip on how to do them?\r<BR>\n" );
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document.write( "Determine the number of solutions to the quadratic equation using the discriminant to determine if the answers are real or complex. (no need to find the roots, just the numer & solution type)\r<BR>\n" );
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document.write( "i. 2x^2+5x+5=0\r<BR>\n" );
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document.write( "ii. 3z^2+z-1=0\r<BR>\n" );
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document.write( "Many thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40631 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=40631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Determine the number of solutions to the quadratic equation using the discriminant to determine if the answers are real or complex. (no need to find the roots, just the numer & solution type)<BR>\n" );
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document.write( "The discriminant of a quadratic equation written in standard form<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b%5E2-4ac%29 ALIGN=MIDDLE  ALT=\"highlight%28b%5E2-4ac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Notice that this is just the inside of the square root in the quadratic equation.<BR>\n" );
document.write( "If the discriminant is positive there are 2 real solutions.<BR>\n" );
document.write( "If the discriminant is 0 there is one real solution.<BR>\n" );
document.write( "If the discriminant is negative there are 2 complex solutions.<BR>\n" );
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document.write( "i. 2x^2+5x+5=0<BR>\n" );
document.write( "a=2, b=5,c=5 The discriminant is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%29%5E2-4%282%29%285%29 ALIGN=MIDDLE  ALT=\"%285%29%5E2-4%282%29%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-40 ALIGN=MIDDLE  ALT=\"25-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15 ALIGN=MIDDLE  ALT=\"-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >  negative.  There are 2 complex solutions.<BR>\n" );
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document.write( "ii. 3z^2+z-1=0<BR>\n" );
document.write( "a=3, b=1,c=-1 The discriminant is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%5E2-4%283%29%28-1%29 ALIGN=MIDDLE  ALT=\"%281%29%5E2-4%283%29%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B12 ALIGN=MIDDLE  ALT=\"1%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > positive. There are two real solutions.<BR>\n" );
document.write( "Happy Calculating!!!<BR>\n" );
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