document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237493>Question 237493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What value of K will the roots of the equation 2x^2-3x+K=0 be imaginary?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174770 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is 2x^2 - 3x + k = 0\r<BR>\n" );
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document.write( "standard form of equation is ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "in this equation:\r<BR>\n" );
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document.write( "a = 2<BR>\n" );
document.write( "b = -3<BR>\n" );
document.write( "c = k\r<BR>\n" );
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document.write( "discriminant is b^2 - 4ac\r<BR>\n" );
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document.write( "if the discriminant is negative, then the roots will be imaginary.\r<BR>\n" );
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document.write( "b^2 - 4ac becomes:\r<BR>\n" );
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document.write( "(-3)^2 - 4*2*k\r<BR>\n" );
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document.write( "this equals 9 - 8*k\r<BR>\n" );
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document.write( "solve for k to get:\r<BR>\n" );
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document.write( "k = 9/8\r<BR>\n" );
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document.write( "if k is greater than 9/8, then the discriminant will be negative and the roots will be imaginary.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "let k = 9/8\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "2x^2 - 3x + 9/8 = 0\r<BR>\n" );
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document.write( "solve for the roots to get:\r<BR>\n" );
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document.write( "x = (-b +/- sqrt(b^2-4ac))/2a\r<BR>\n" );
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document.write( "a = 2<BR>\n" );
document.write( "b = -3<BR>\n" );
document.write( "c = 9/8\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "x = -(9/8) +/- sqrt(9 - 4*2*9/8) / 4\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "x = (-9/8) +/- sqrt(9-9) / 4 = real roots.\r<BR>\n" );
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document.write( "now let c = 10/8\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "x = (-10/8) +/- sqrt (9 - 4*2*10/8) / 4\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "x = (-10/8) +/- sqrt (9 - 10) / 4\r<BR>\n" );
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document.write( "sqrt (9-10) is negative causing the roots to be imaginary.\r<BR>\n" );
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document.write( "answer is that k > 9/8 makes the roots imaginary.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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