document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=574632>Question 574632</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the roots of the polynomial,\" x^4-81=0\"? I don't understand this because supposedly with a degree of four there are exactly four roots to this polynomial, but there are only two terms.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369184 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=369184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tricky!\r<BR>\n" );
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document.write( "Let's not solve for X right away, but X^2.  Does that help?<BR>\n" );
document.write( "X^4-81=0<BR>\n" );
document.write( "(x^2 - )(X^2 + ) = 0  (We need to find two factors of 81.)<BR>\n" );
document.write( "9x9 = 81  Aha!<BR>\n" );
document.write( "(X^2 - 9)(X^2 + 9) = 0  Now factor as you would normally, but using X^2 as terms\r<BR>\n" );
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document.write( "Left paren first:<BR>\n" );
document.write( "X^2 - 9 = 0  <BR>\n" );
document.write( "X^2 = 9<BR>\n" );
document.write( "Sqrt(X^2) = Sqrt(9)<BR>\n" );
document.write( "X = 3 or -3\r<BR>\n" );
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document.write( "Right paren:<BR>\n" );
document.write( "X^2 + 9 = 0<BR>\n" );
document.write( "X^2 = -9<BR>\n" );
document.write( "Depending on your grade, either this is impossible - or an irrational possibility. ;-) I'm going to guess you're not into irrational numbers yet.  But if you are, you can still take it from here.  By the way, this is how we get more than the two solutions we did above.\r<BR>\n" );
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document.write( "Checking:<BR>\n" );
document.write( "X^4 - 81 = 0<BR>\n" );
document.write( "(3)^4 - 81 = 0<BR>\n" );
document.write( "81 - 81 = 0  Correct!\r<BR>\n" );
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document.write( "AND<BR>\n" );
document.write( "X^4 - 81 = 0<BR>\n" );
document.write( "(-3)^4 - 81 = 0<BR>\n" );
document.write( "81 - 81 = 0  Correct! </SPAN>\n" );
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