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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
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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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use rational roots theorem and synthetic division:
f(x)=x^4-10x³+36x²-54x+27
...0...|....1......-10......36.....-54......27......
...1...|....1.......-9.......27.....-27......0 (1 is a root)
...2...|....1.......-7.......13.....-1.........
...3...|....1.......-6........9.......0...........(3 is a root)
f(x)=(x-1)(x-3)(x^2-6x+9)=(x-1)(x-3)(x-3)(x-3)
zeros are: 1 and 3 (multiple of 3)
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h(x)=x^4-4x³-9x²+16x+20
...0...|....1......-4......-9.......16......20......
...1...|....1......-3......-12......4.......24.........
...2...|....1......-2......-13....-10......0 (2 is a root)
...3...|....1.......1......-10....-40
...4...|....1.......2......-5......-30
...5...|....1.......3.......2........0 (5 is a root)
h(x)=(x-2)(x-5)(x^2+3x+2)=(x-2)(x-5)(x+1)(x+2)
zeros are: -1, -2, 2, 5
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