document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388614>Question 388614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2. A curve has its equations y=x³-kx²-16x+32\r<BR>\n" );
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document.write( "2(a). If the curve crosses the x-axis at A(2,0), find k.<BR>\n" );
document.write( "2(b). The point B(p,35) also lies on this curve, find the value of p.<BR>\n" );
document.write( "2(c). Calculate the size of the angle between the line AB and the x-axis in the positive direction. Give the answer to the nearest degree. \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275055 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2%5E3+-+k%2A2%5E2+-+16%2A2+%2B+32+=+8-4k ALIGN=MIDDLE  ALT=\"0+=+2%5E3+-+k%2A2%5E2+-+16%2A2+%2B+32+=+8-4k\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or 4k = 8, or k = 2.\r<BR>\n" );
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document.write( "(b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35+=+p%5E3+-+2p%5E2-16p+%2B+32 ALIGN=MIDDLE  ALT=\"35+=+p%5E3+-+2p%5E2-16p+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+p%5E3+-+2p%5E2-16p+-+3 ALIGN=MIDDLE  ALT=\"0+=+p%5E3+-+2p%5E2-16p+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The roots of this equation are -3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285+%2B-+sqrt%2829%29%29%2F2+ ALIGN=MIDDLE  ALT=\"%285+%2B-+sqrt%2829%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Therefore the points are<BR>\n" );
document.write( " (-3, 35), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285+%2B-+sqrt%2829%29%29%2F2+ ALIGN=MIDDLE  ALT=\"%285+%2B-+sqrt%2829%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 35). (Three possibilities!)\r<BR>\n" );
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document.write( "(c) To find the inclination <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the line AB, compute for the slope m of the line AB, and use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+tan%28theta%29 ALIGN=MIDDLE  ALT=\"m+=+tan%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+tan%5E%28-1%29%28m%29 ALIGN=MIDDLE  ALT=\"theta+=+tan%5E%28-1%29%28m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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