document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80633>Question 80633</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131444417/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> We are solving quadratic equation. I tried to sole this problem, but I'm having some trouble. Please help me solve this quadratic equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3-1=0 ALIGN=MIDDLE  ALT=\"8x%5E3-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Any help will be appreciated.  Thank you,<BR>\n" );
document.write( "                                Jennie <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57818 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve this quadratic equation: 8x^3-1 = 0<BR>\n" );
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document.write( "You should recognize this as \"the difference of cubes\" which come under a section<BR>\n" );
document.write( "referred to as \"Special Factoring Formulas\", given in a book that I have as:<BR>\n" );
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document.write( "u^3 - v^3 = (u - v)(u^2 + uv + v^2)<BR>\n" );
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document.write( "in your problem u^3 = 8x^3 and -v^3 = -1<BR>\n" );
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document.write( "So we have:<BR>\n" );
document.write( "(8x^3 - 1) = (2x - 1)(4x^2 + 2x + 1)<BR>\n" );
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document.write( "You check this for yourself: multiply (2x-1) * (4x^2 + 2x +1) you should get the<BR>\n" );
document.write( "original equation<BR>\n" );
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document.write( "Look in the index of your algebra book under \"difference of cubes\" you should see the special factor formulas there<BR>\n" );
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document.write( "Added after receiving inquiry from student:<BR>\n" );
document.write( " (2x-1)(4x^2 + 2x + 1) = 0<BR>\n" );
document.write( "The 1st factor:<BR>\n" );
document.write( "2x - 1 = 0<BR>\n" );
document.write( "2x = +1<BR>\n" );
document.write( "x = 1/2<BR>\n" );
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document.write( "The other factor: (4x^2 + 2x + 1),= 0,  has no real roots The discriminant<BR>\n" );
document.write( "of the equation is b^2 - 4*a*c, as I am sure you know.<BR>\n" );
document.write( "In this case, a=4; b=2; c=1:    2^2 - 4*4*1 =  -12, remember when the<BR>\n" );
document.write( "discriminant is negative it has no real roots<BR>\n" );
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document.write( "A graph would look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+8x%5E3+-+1%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+8x%5E3+-+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that it crosses the x axis only at +.5\r<BR>\n" );
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