document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762677>Question 762677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) show that the equation 0.25x squared - 0.7+ 1.5 =0 does not have any real roots.\r<BR>\n" );
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document.write( "b) the line y=2x - 5 and the curve xsquared + xy = 2 intersects at the point A and B, show that the equation to find the points A and B is givin by: <BR>\n" );
document.write( "3xsquared - 5x - 2 = 0.\r<BR>\n" );
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document.write( "Hence find the coordinates of A and B. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464119 by </B><A HREF=/tutors/aboutme.mpl?userid=malglu><B>malglu(63)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=malglu><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=464119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use the determinant b^2-4ac<BR>\n" );
document.write( "which is <BR>\n" );
document.write( "(-0.7)^2  - 4 x 0.25 x 1.5<BR>\n" );
document.write( "this = -1.01<BR>\n" );
document.write( "when the determinant is less then 0 then the roots are not real.\r<BR>\n" );
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document.write( "the points A and B obviously are on both the line and the curve.  to find them we neeed to put 2x -5 in the equation of the curve whenever it has y\r<BR>\n" );
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document.write( "x^2 + (2x-5)x -2 =0\r<BR>\n" );
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document.write( "i have then -2 on each side so i can equal the equation to 0.  the equation is now<BR>\n" );
document.write( "x^2 + 2x^2 -5x -2=0<BR>\n" );
document.write( "3x^2 -5x -2 =0\r<BR>\n" );
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document.write( "now find the roots of this equation<BR>\n" );
document.write( "i used the formula to get x=2 and x= -1/3\r<BR>\n" );
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document.write( "put these values into any of the original equtions to get the y co-ordinates.\r<BR>\n" );
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document.write( "y=2x-5, so when x = 2 y = -1 and when x=-1/3 y=-17/3.  these are the points A and B\r<BR>\n" );
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document.write( " </SPAN>\n" );
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