document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137577>Question 1137577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what value(s) of k will the function h(x)=4x^2-kx +25 have only one zero? Explain your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755453 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=755453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe you would use the quadratic formula to solve this.\r<BR>\n" );
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document.write( "that formula is:\r<BR>\n" );
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document.write( "x = (-b plus or minus sqrt(b^2 - 4ac) / (2a).\r<BR>\n" );
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document.write( "the discriminant is the piece under the square root sign.\r<BR>\n" );
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document.write( "that piece is b^2 - 4ac.\r<BR>\n" );
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document.write( "when that equals to 0, there will be only one root to the quadratic equation.\r<BR>\n" );
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document.write( "your equation is h(x) = 4x^2 - kx + 25.\r<BR>\n" );
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document.write( "set h(x) equal to 0 and the equation becomes 4x^2 - kx + 25 = 0\r<BR>\n" );
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document.write( "the equation is now in standard form, where:\r<BR>\n" );
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document.write( "a = 4<BR>\n" );
document.write( "b = -k<BR>\n" );
document.write( "c = 25\r<BR>\n" );
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document.write( "the discriminant in the quadratic formula is b^2 - 4ac.\r<BR>\n" );
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document.write( "set that equal to 0 and you get b^2 - 4ac = 0.\r<BR>\n" );
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document.write( "replace b with -k and a with 4 and c with 25 and you get:\r<BR>\n" );
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document.write( "(-k)^2 - 4*4*25 = 0\r<BR>\n" );
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document.write( "simplify to get k^2 - 400 = 0\r<BR>\n" );
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document.write( "solve for k^2 to get k^2 = 400\r<BR>\n" );
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document.write( "solve for k to get k = plus or minus 20.\r<BR>\n" );
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document.write( "if k is plus 20, the original equation becomes h(x) = 4x^2 - 20x + 25\r<BR>\n" );
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document.write( "if k is minus 20, the original equation becomes h(x) = 4x^2 + 20x + 25\r<BR>\n" );
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document.write( "to graph, set y = h(x), so that the equations become y = rather than h(x) =.\r<BR>\n" );
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document.write( "the following graph shows you that you will get one root when k is equal to plus or minus 20.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/032831.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the key to finding only one root is that the discriminant has to be equal to 0.\r<BR>\n" );
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document.write( "the discriminant is the part under the square root sign of the quadratic formula.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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