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find the roots of the following polynomial 1) x3-6x²+11x-6=0​

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From the rational root theorem, actor out x-1 from x³ - 6x² + 11x -6 0:

(x-1) (x2-5x+6)

Factor further (x2-5x+6): (x 3) (x-2)

The factors of the polynomial:
(x-1) (x-3) (x-2)=0

x-1=0 , x-3=0 , x-2=0
x=1 , x=3 , x=2

The roots are: 1 , 2 , 3

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