document.write( "Question 208412This question is from textbook ALGERA
\n" ); document.write( ": pls. help me to solve this equation I really dont know how to get the root
\n" ); document.write( "Using the Descartes’ Rule of signs, give by means of tabulation, all the possible combinations of the number of positive roots, negative roots and imaginary roots.
\n" ); document.write( "Find all roots by synthetic division and using the remainder theorem and the factor theorem.
\n" ); document.write( "1.) x^4-4x^3+4x-1=0
\n" ); document.write( "2.) 4x^4+8x^3-7x^2-21-9=0
\n" ); document.write( " thank you very much for your help \n" ); document.write( "
Algebra.Com's Answer #157643 by stanbon(75887)\"\" \"About 
You can put this solution on YOUR website!
Find all roots by synthetic division and using the remainder theorem and the factor theorem.
\n" ); document.write( "1.) x^4-4x^3+4x-1=0
\n" ); document.write( "Since the coefficients add up to zero, one is a root.
\n" ); document.write( "Use synthetic division to find others:
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\n" ); document.write( "1)....1....-4.....0...4....-1
\n" ); document.write( ".......1....-3....-3...1...|..0\r
\n" ); document.write( "\n" ); document.write( "The Quotient is f(x) = x^3 - 3x^2 -3x + 1
\n" ); document.write( "f(-1) = -1 -3 +3 + 1 = 0
\n" ); document.write( "so, -1 is a root
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\n" ); document.write( "-1).... 1....-3....-3....1
\n" ); document.write( ".........1.....-4....1...|..0\r
\n" ); document.write( "\n" ); document.write( "Now use the quadratic formula to find
\n" ); document.write( "the roots of x^2 -4x + 1\r
\n" ); document.write( "\n" ); document.write( "x = [4 +- sqrt(16 - 4*1*!)]/2
\n" ); document.write( "x = [4 +- sqrt(12)]/2
\n" ); document.write( "x = 2 + sqrt(3) or x = 2 - sqrt(3)
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "So there you have the 4 roots.
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\n" ); document.write( "\n" ); document.write( "2.) 4x^4+8x^3-7x^2-21-9=0
\n" ); document.write( "I graphed f(x) to find a Real Number root to start the process.
\n" ); document.write( "There are no \"neat\" roots so I'll leave this to you as it is
\n" ); document.write( "getting too late here.
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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