document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=421852>Question 421852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can u please help me solve this question?\r<BR>\n" );
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document.write( "1.The straight line y=3-4x does not intersect the curve y=5x^2-x+q.Find the range of values of q. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #294540 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=294540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For these types of problems, it often helps to graph the functions for some values of q (even though it is quite possible to solve without graphing).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-30%2C30%2C+3-4x%2C+5x%5E2+-+x%2C+5x%5E2+-+x+%2B+5%2C+5x%5E2+-+x+-+5%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can see from the graph that there is some constant q = C such that the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5x%5E2+-+x+%2B+C ALIGN=MIDDLE  ALT=\"y+=+5x%5E2+-+x+%2B+C\"   DISABLED_style= \"max-width:90%; height:auto;\" > intersects <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3+-+4x ALIGN=MIDDLE  ALT=\"y+=+3+-+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > at exactly one point. Also, when q < C, the graphs will intersect at two points, and for q > C, the graphs do not intersect. We wish to find the value of C.\r<BR>\n" );
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document.write( "This occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+-+x+%2B+C+=+3+-+4x ALIGN=MIDDLE  ALT=\"5x%5E2+-+x+%2B+C+=+3+-+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+%2B+3x+%2B+%28C-3%29+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2+%2B+3x+%2B+%28C-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The graphs intersect at only one point when the discriminant is zero, i.e.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+-+4%285%29%28C-3%29+=+0 ALIGN=MIDDLE  ALT=\"9+-+4%285%29%28C-3%29+=+0\"   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=9+-+20%28C-3%29+=+0 ALIGN=MIDDLE  ALT=\"9+-+20%28C-3%29+=+0\"   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=9+-+20C+%2B+60+=+0 ALIGN=MIDDLE  ALT=\"9+-+20C+%2B+60+=+0\"   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=20C+=+69 ALIGN=MIDDLE  ALT=\"20C+=+69\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+69%2F20 ALIGN=MIDDLE  ALT=\"C+=+69%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therefore, all values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+%3E+69%2F20 ALIGN=MIDDLE  ALT=\"q+%3E+69%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > satisfy. </SPAN>\n" );
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