document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252418>Question 252418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value(s) of k such that the equation f(x + k) = 0 has two equal real roots.\r<BR>\n" );
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document.write( "f(x) = - (1/2)x^2 - 5x + 4\r<BR>\n" );
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document.write( "please show steps, thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184348 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=184348\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the value(s) of k such that the equation f(x + k) = 0 has two equal real roots. <BR>\n" );
document.write( "f(x) = - (1/2)x^2 - 5x + 4 <BR>\n" );
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document.write( "Find f(x+k):<BR>\n" );
document.write( "f(x+k) = (1/2)(x+k)^2-5(x+k)+4<BR>\n" );
document.write( "f(x+k) = (1/2)(x^2+2kx+k^2 - 5x-5k+4<BR>\n" );
document.write( "f(x+k) = (1/2)(x^2+(2k-5)x + (k^2-5k+4)<BR>\n" );
document.write( "f(x+k) = (1/2)x^2 + [(2k-5)/2]x + [k^2-5k+4]/2<BR>\n" );
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document.write( "You have a quadratic with<BR>\n" );
document.write( "a = 1/2<BR>\n" );
document.write( "b = (2k-5)/2<BR>\n" );
document.write( "c = (k^2-5k+4)/2<BR>\n" );
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document.write( "Determine when f(x+k) will have two equal real roots.<BR>\n" );
document.write( "That happens when the discriminant is zero<BR>\n" );
document.write( "Solve:<BR>\n" );
document.write( "b^2-4ac = 0<BR>\n" );
document.write( "[(2k-5)/2]^2 - 4*(1/2)(k^2-5k+4)/2 = 0<BR>\n" );
document.write( "[(1/4)(4k^2-20k+25)]-[k^2-5k+4] = 0<BR>\n" );
document.write( "[k^2-5k+(25/4)]-[k^2-5k+4] = 0<BR>\n" );
document.write( "9/4 = 0<BR>\n" );
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document.write( "Well, I get a contradiction but I may have made<BR>\n" );
document.write( "an arithmetic mistake somewhere along the line.<BR>\n" );
document.write( "Check it out and see what you get.<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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