document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993457>Question 993457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For what value of B does the function <BR>\n" );
document.write( "F(x)=-3x^2+Bx-4<BR>\n" );
document.write( "have only 1 x-intercept. Find all possible values of B and leave your answer in exact form.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612823 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "For what value of B does the function F(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2%2BBx-4 ALIGN=MIDDLE  ALT=\"-3x%5E2%2BBx-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "have only 1 x-intercept. Find all possible values of B and leave your answer in exact form. <BR>\n" );
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document.write( "It may happen if and only if two real roots of the quadratic polynomial &nbsp;F(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3x%5E2%2BBx-4 ALIGN=MIDDLE  ALT=\"-3x%5E2%2BBx-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;merge into one \r<BR>\n" );
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document.write( "real root of multiplicity &nbsp;2. &nbsp;It is the case when the plot of the quadratic polynomial touches &nbsp;x-axis.\r<BR>\n" );
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document.write( "In turn, &nbsp;a necessary and a sufficient condition for it is vanishing the discriminant of the polynomial, &nbsp;which is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5E2 ALIGN=MIDDLE  ALT=\"B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 4*(-3)*(-4) = 0, &nbsp;&nbsp;&nbsp;&nbsp;or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5E2 ALIGN=MIDDLE  ALT=\"B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 16*3.\r<BR>\n" );
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document.write( "It gives &nbsp;&nbsp;B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;and/or &nbsp;&nbsp;B = - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "At these values of B &nbsp;&nbsp;F(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28sqrt%283%29%2Ax+-+2%29%5E2 ALIGN=MIDDLE  ALT=\"-%28sqrt%283%29%2Ax+-+2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;or &nbsp;&nbsp;F(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28sqrt%283%29%2Ax+%2B+2%29%5E2 ALIGN=MIDDLE  ALT=\"-%28sqrt%283%29%2Ax+%2B+2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;correspondingly.\r<BR>\n" );
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document.write( "<U>Answer</U>. &nbsp;&nbsp;B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;and/or &nbsp;&nbsp;B = - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-5.5%2C+5.5%2C+-10.5%2C+5.5%2C%0D%0A++++++++++-%28sqrt%283%29%2Ax+-+2%29%5E2%2C%0D%0A++++++++++-%28sqrt%283%29%2Ax+%2B+2%29%5E2%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Plots <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28sqrt%283%29%2Ax+-+2%29%5E2 ALIGN=MIDDLE  ALT=\"-%28sqrt%283%29%2Ax+-+2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in red) and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28sqrt%283%29%2Ax+%2B+2%29%5E2 ALIGN=MIDDLE  ALT=\"-%28sqrt%283%29%2Ax+%2B+2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in green)\r<BR>\n" );
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