document.write( "Question 969998: Find all real zeros of the functions f(x)=x^4-10x³+36x²-54x+27 and h(x)=x^4-4x³-9x²+16x+20 \n" ); document.write( "
Algebra.Com's Answer #593036 by lwsshak3(11628)\"\" \"About 
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Find all real zeros of the functions f(x)=x^4-10x³+36x²-54x+27 and h(x)=x^4-4x³-9x²+16x+20
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\n" ); document.write( "use rational roots theorem and synthetic division:
\n" ); document.write( " f(x)=x^4-10x³+36x²-54x+27
\n" ); document.write( "...0...|....1......-10......36.....-54......27......
\n" ); document.write( "...1...|....1.......-9.......27.....-27......0 (1 is a root)
\n" ); document.write( "...2...|....1.......-7.......13.....-1.........
\n" ); document.write( "...3...|....1.......-6........9.......0...........(3 is a root)
\n" ); document.write( " f(x)=(x-1)(x-3)(x^2-6x+9)=(x-1)(x-3)(x-3)(x-3)
\n" ); document.write( "zeros are: 1 and 3 (multiple of 3)
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\n" ); document.write( "h(x)=x^4-4x³-9x²+16x+20
\n" ); document.write( "...0...|....1......-4......-9.......16......20......
\n" ); document.write( "...1...|....1......-3......-12......4.......24.........
\n" ); document.write( "...2...|....1......-2......-13....-10......0 (2 is a root)
\n" ); document.write( "...3...|....1.......1......-10....-40
\n" ); document.write( "...4...|....1.......2......-5......-30
\n" ); document.write( "...5...|....1.......3.......2........0 (5 is a root)
\n" ); document.write( "h(x)=(x-2)(x-5)(x^2+3x+2)=(x-2)(x-5)(x+1)(x+2)
\n" ); document.write( "zeros are: -1, -2, 2, 5 \n" ); document.write( "
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