document.write( "Question 973379: given the function f(x)=x^4+3x^3-6x^2+12x-40|. find all the roots of the polynomial algebraically \n" ); document.write( "
Algebra.Com's Answer #595658 by lwsshak3(11628)\"\" \"About 
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given the function f(x)=x^4+3x^3-6x^2+12x-40|. find all the roots of the polynomial algebraically.
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\n" ); document.write( "solve by rational roots theorem:
\n" ); document.write( "f(x)=x^4+3x^3-6x^2+12x-40\r
\n" ); document.write( "\n" ); document.write( "...0...|.....1.......3.......-6......12......-40......
\n" ); document.write( "...1...|.....1.......4.......-2......10......-30.......
\n" ); document.write( "...2...|.....1.......5........4......20....... 0..(2 is a root) (2 is also upper boundary)
\n" ); document.write( "======================
\n" ); document.write( "...0...|.....1.......5........4......20.......
\n" ); document.write( "..-1...|.....1......4........0......19..............
\n" ); document.write( "..-2...|.....1......3.......-2......16...............
\n" ); document.write( "..-3...|.....1......2.......-2......14.................
\n" ); document.write( "..-4...|.....1.....1.........0......20...................
\n" ); document.write( "..-5...|.....1.....0.........4.......0...(-5 is a root)\r
\n" ); document.write( "\n" ); document.write( "f(x)=(x-2)(x+5)(x^2+4)
\n" ); document.write( "roots are: -5, 2, and 2 imaginary roots(±2i) \n" ); document.write( "
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