document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211094>Question 211094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) For the quadratic equation kx^2 + 2x + 4 = 0, find the value of k so that<BR>\n" );
document.write( "the roots are equal (there is only one root).<BR>\n" );
document.write( "b) The roots of x^2 + (k + 8)x + 9k = 0 are equal. What are the value(s) of<BR>\n" );
document.write( "k? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159495 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  For the quadratic equation kx^2 + 2x + 4 = 0, find the value of k so that<BR>\n" );
document.write( "the roots are equal (there is only one root).<BR>\n" );
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document.write( "Use the discriminant: a=k; b=2; c=4<BR>\n" );
document.write( "b^2 - 4ac = 0 means equal roots<BR>\n" );
document.write( "2^2 - 4*k*4 = 0<BR>\n" );
document.write( "4 - 16k = 0<BR>\n" );
document.write( "-16k = -4<BR>\n" );
document.write( "k = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%29%2F%28-16%29 ALIGN=MIDDLE  ALT=\"%28-4%29%2F%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "k = +.25 (=a)<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".25x^2 + 2x + 4 = 0<BR>\n" );
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document.write( "get rid of the decimal, multiply by 4<BR>\n" );
document.write( "x^2 + 8x + 16 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x+4)(x+4) = 0<BR>\n" );
document.write( "x = -4 is the single root<BR>\n" );
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document.write( "b) The roots of x^2 + (k + 8)x + 9k = 0 are equal. What are the value(s) of<BR>\n" );
document.write( "k?<BR>\n" );
document.write( "Use the discriminant: a=1; b=(k+8); c=9k<BR>\n" );
document.write( "b^2 - 4ac = 0 means equal roots<BR>\n" );
document.write( "(k+8)^2 - 4*1*(9k) = 0<BR>\n" );
document.write( "k^2 + 16k + 64 - 36k = 0<BR>\n" );
document.write( "k^2 - 20k + 64 = 0<BR>\n" );
document.write( "(k-16)(k-4) = 0<BR>\n" );
document.write( "k = 16<BR>\n" );
document.write( "and<BR>\n" );
document.write( "k = 4<BR>\n" );
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document.write( "When k=16 then b=24, and c=144 (9*16)<BR>\n" );
document.write( "x^2 + 24x + 144<BR>\n" );
document.write( "Factors<BR>\n" );
document.write( "(x+12)(x+12) = 0<BR>\n" );
document.write( "x = -12 is the single root<BR>\n" );
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document.write( "When k=4, then b=12, and c=36<BR>\n" );
document.write( "x^2 + 12x + 36<BR>\n" );
document.write( "Factors <BR>\n" );
document.write( "(x+6)(x+6) = 0<BR>\n" );
document.write( "x = -6 is the single root </SPAN>\n" );
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