document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=810574>Question 810574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> tell if the equation has two solutions, one solution, or no real solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #488454 by </B><A HREF=/tutors/aboutme.mpl?userid=Charles3475><B>Charles3475(23)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Charles3475><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=Charles3475><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=488454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In algebra, the discriminant of a polynomial is a function of its coefficients, typically denoted Greek letter Delta (&#916;).The discriminant of the quadratic polynomial\r<BR>\n" );
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document.write( "ax^2+bx+c\r<BR>\n" );
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document.write( "is\r<BR>\n" );
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document.write( "&#916;=b^2-4ac\r<BR>\n" );
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document.write( "A quadratic polynomial with real coefficients has real roots (solutions when the function is equal to zero) if and only if the discriminant is non-negative, and these roots are distinct if and only if it is positive (not zero). Thus\r<BR>\n" );
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document.write( "	&#916; > 0: 2 distinct real roots<BR>\n" );
document.write( "	&#916; < 0: 2 distinct complex roots<BR>\n" );
document.write( "	&#916; = 0: 1 real root with multiplicity 2\r<BR>\n" );
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document.write( "A complex root is not a real root. The square root of negative 1 (i=&#8730;(-1)) is used for all complex numbers. This number is called \"i\", standing for \"imaginary\", because i is not \"real\".\r<BR>\n" );
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document.write( "For your question: tell if the equation has two solutions, one solution, or no real solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a=1<BR>\n" );
document.write( "b=-3<BR>\n" );
document.write( "c=4\r<BR>\n" );
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document.write( "The discriminant equals b^2-(4)(a)(c) = (-3)^2-(4)(1)(4) = 9 - 16 = -7\r<BR>\n" );
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document.write( "As the discriminant is negative there are no real roots. <BR>\n" );
document.write( "There are two complex roots.\r<BR>\n" );
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document.write( "All of this falls out of the quadratic formula. The discriminant is part of the formula. Take a look!  </SPAN>\n" );
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