document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71000>Question 71000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the range of values for p such that 3X^2 + 3px + p^2 = 1 has real roots </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50738 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=50738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the range of values for p such that<BR>\n" );
document.write( "  3X^2 + 3px + p^2 = 1 has real roots<BR>\n" );
document.write( "3X^2+3PX+(P^2-1)=0<BR>\n" );
document.write( "DISCRIMINANT = (3P)^2-4(3)(P^2-1)=9P^2-12P^2+12= 12-3P^2<BR>\n" );
document.write( "HENCE FOR REAL ROOTS<BR>\n" );
document.write( "12-3P^2>=0<BR>\n" );
document.write( "4-P^2>=0<BR>\n" );
document.write( "4>=P^2<BR>\n" );
document.write( "2>=|P|<BR>\n" );
document.write( "|P|<=2<BR>\n" );
document.write( "RANGE OF P IS [-2,2] </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );