document.write( "Question 469096: Use the rational zero theorem and quotient polynomials to find all roots of the given equation\r
\n" ); document.write( "\n" ); document.write( "x(^4)+ x(^3)+x(^2)+3x-6=0
\n" ); document.write( "(x to the fourth plus x to the third plus x squared plus 3x minus 6 equals 0) \n" ); document.write( "
Algebra.Com's Answer #322072 by lwsshak3(11628)\"\" \"About 
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Use the rational zero theorem and quotient polynomials to find all roots of the given equation
\n" ); document.write( "x(^4)+ x(^3)+x(^2)+3x-6=0
\n" ); document.write( "(x to the fourth plus x to the third plus x squared plus 3x minus 6 equals 0)
\n" ); document.write( "...
\n" ); document.write( "P(x)=x^4+x^3+x^2+3x-6
\n" ); document.write( "Factors of p=6: ±1, ±2, ±3, ±3, ±6
\n" ); document.write( "Factors of q=1: ±1
\n" ); document.write( "possible rational roots, p/q: ±1, ±2, ±3, ±3, ±6
\n" ); document.write( "..
\n" ); document.write( "Using synthetic division to find roots:
\n" ); document.write( "0)......1....1....1....3....-6
\n" ); document.write( "1)......1....2....3....6.....0 (root=1)
\n" ); document.write( "p(x)=(x-1)(x^3+2x^2+3x+6)
\n" ); document.write( "Try again:
\n" ); document.write( "0)......1....2....3....6
\n" ); document.write( "-1)....1....1....2....4
\n" ); document.write( "-2)....1....0....3....0 (root=-2)
\n" ); document.write( "p(x)=(x-1)(x+1)(x^2+3)
\n" ); document.write( "x^2+3=0
\n" ); document.write( "x=±√-3
\n" ); document.write( "zeros: -2, 1 and two complex roots, ±√-3 \n" ); document.write( "
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