document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857230>Question 857230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the quadratic equation x^2 -x +3 = k has real roots, find the range of values of k.\r<BR>\n" );
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document.write( "The answer is k is greater than or equal to 11/4. And what I get is k = 11/4. I don't understand why greater than or equal to is used instead of equal to. Thanks for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516427 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=516427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "If the quadratic equation x^2 -x +3 = k has real roots, find the range of values of k. <BR>\n" );
document.write( "The answer is k is greater than or equal to 11/4. And what I get is k = 11/4. I don't understand why greater than or equal to is used instead of equal to<BR>\n" );
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document.write( "A:<BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a &#8800; 0.<BR>\n" );
document.write( "The roots are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Quadratic Formula)<BR>\n" );
document.write( "The roots are real if the expression inside the square root is non-negative.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-x+%2B3+=+k ALIGN=MIDDLE  ALT=\"x%5E2+-x+%2B3+=+k\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+%2B+%283+-+k%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B+%283+-+k%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 1, b = -1 and c = 3 - k<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac+=+%28-1%29%5E2+-+4%281%29%283+-+k%29+%3E=+0 ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac+=+%28-1%29%5E2+-+4%281%29%283+-+k%29+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4k+-+11+%3E=+0+ ALIGN=MIDDLE  ALT=\"4k+-+11+%3E=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k+%3E=+11%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28k+%3E=+11%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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