document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=628470>Question 628470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.  find all the roots of x3+2x2+2x+1<BR>\n" );
document.write( "2.  if 2-i is a root of 3x3-11x2+11x+5, then what are its other roots?<BR>\n" );
document.write( "3.  find the negative root of x2-3+0 to the nearest tenth<BR>\n" );
document.write( "4.  how long will it take a population with a 10% annual growth rate to double?<BR>\n" );
document.write( "5.  how many roots does x6=3x5+1 have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395655 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=395655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. find all the roots of x^3+2x^2+2x+1<BR>\n" );
document.write( "Since f(-1) = 0, -1 is a root.<BR>\n" );
document.write( "Use synthetic division to find other roots.<BR>\n" );
document.write( "-1)....1....2....2....1<BR>\n" );
document.write( "........1....1....1...|..0\r<BR>\n" );
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document.write( "Quotient: x^2+x+1 <BR>\n" );
document.write( "Use the quadratic formula:<BR>\n" );
document.write( "x = [-1 +- sqrt(1-4*1*1)]/2 = [-1+-sqrt(-3)]/2 = (-1/2)+-isqrt(3)/2<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "2. if 2-i is a root of 3x3-11x2+11x+5, then what are its other roots?<BR>\n" );
document.write( "Since the coefficients are Real, 2+i is also a root.<BR>\n" );
document.write( "Also x = -1/3 is a root.<BR>\n" );
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document.write( "3. find the negative root of x^2-3+0 to the nearest tenth<BR>\n" );
document.write( "Comment: Not an equation.<BR>\n" );
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document.write( "4. how long will it take a population with a 10% annual growth rate to double?<BR>\n" );
document.write( "Solve: 2P = p(1.1)^t<BR>\n" );
document.write( "1.1^t = 2<BR>\n" );
document.write( "t = log(2)/log(1.1) = 7.27 years<BR>\n" );
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document.write( "5. how many roots does x6=3x5+1 have?<BR>\n" );
document.write( "Ans: six<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "====================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );