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 #516425 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=516425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Maybe the wording has thrown your concept off?  Maybe you forgot that the question was about \"range\", and you momentarily mistook at as something else?\r<BR>\n" );
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document.write( "The wording, the quadratic equation x^2 -x +3 = k has real roots, is like f(x)=x^2-x+3, and then renaming f(x) as k.<BR>\n" );
document.write( "NOW, what is the range for f(x)?  That is all the question asks.\r<BR>\n" );
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document.write( "Note that your function based on qualitative familiarity with this type of function, has a minimum and is concave upward.  The vertex is a MINIMUM; all values of the function are GREATER THAN OR EQUAL to the minimum value, which you found as 11/4. </SPAN>\n" );
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