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 #294539 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=294539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I've never seen a problem like this before, but I think I have a solution, although it may not be the preferred way of dealing with this type of problem.\r<BR>\n" );
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document.write( "If the equation of y = 5x^2 - x + q is to intersect with the line y = 3-4x, then to find the points of intersection, we would set y equal to 3-4x and solve for x.\r<BR>\n" );
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document.write( "accordingly, we set 5x^2 - x + q = 3 - 4x\r<BR>\n" );
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document.write( "if we subtract 3 from both sides of the equation and we add 4x to both sides of the equation, we get:\r<BR>\n" );
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document.write( "5x^2 + 3x - 3 + q = 0\r<BR>\n" );
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document.write( "we can rearrange the terms to get:\r<BR>\n" );
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document.write( "5x^2 + 3x - (q+3) = 0\r<BR>\n" );
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document.write( "the standard form of a quadratic equation is ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "in our equation:\r<BR>\n" );
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document.write( "a = 5<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "c = (q+3)\r<BR>\n" );
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document.write( "we find the piece parts of the quadratic formula as follows:\r<BR>\n" );
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document.write( "2a = 10<BR>\n" );
document.write( "-b = -3<BR>\n" );
document.write( "4ac = 4*5*(q-3) = 20q - 60<BR>\n" );
document.write( "b^2 = 9<BR>\n" );
document.write( "b^2 - 4ac = 9 - 20q + 60- = 69-20q<BR>\n" );
document.write( "the discriminant is equal to 69 - 20q<BR>\n" );
document.write( "in order for there to be real roots to this equation, the discriminant has to be >= 0\r<BR>\n" );
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document.write( "set 69-20q >= 0 and solve for q<BR>\n" );
document.write( "add 20q to both sides of this equation to get 69 >= 20q<BR>\n" );
document.write( "divide both sides of this equation by 20 to get 69/20 >= q<BR>\n" );
document.write( "commute this equation to get q <= 69/20<BR>\n" );
document.write( "simplify this to get q <= 3.45\r<BR>\n" );
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document.write( "if q <= 3.45, then we WILL get an intersection of the graph of the equation y = 3 - 4x with the graph of the equation y = 5x^2 - x + q\r<BR>\n" );
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document.write( "conversely, if q > 3.45, then we WILL NOT get an intersection of the graph of the equation y = 3 - 4x with the graph of the equation y = 5x^2 - x + q\r<BR>\n" );
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document.write( "the following graph sets q equal to 3.45\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2%2C3%2C-10%2C10%2C3-4x%2C5x%5E2-x%2B3.45%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2%2C3%2C-10%2C10%2C3-4x%2C5x%5E2-x%2B3.45%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the following graph sets q equal to 4 which is greater than 3.45\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2%2C3%2C-10%2C10%2C3-4x%2C5x%5E2-x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2%2C3%2C-10%2C10%2C3-4x%2C5x%5E2-x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the following graph sets q equal to 3 which is less than 3.45\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-2%2C3%2C-10%2C10%2C3-4x%2C5x%5E2-x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-2%2C3%2C-10%2C10%2C3-4x%2C5x%5E2-x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that when q <= 3.45, the 2 graphs intersect, and you can see that when q > 3.45, the 2 graphs do not intersect.\r<BR>\n" );
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document.write( "in order for there to be a real solution to the intersection of the graph of the 2 equations, the roots of the resulting quadratic equation had to be real.\r<BR>\n" );
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document.write( "in order for them to be real, the discriminant had to be >= 0.\r<BR>\n" );
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document.write( "that led to the solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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