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  • find the integral roots of the polynomial x^3-6x^2+11x-6 .

find the integral roots of the polynomial x^3-6x^2+11x-6 .

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solution: Let f(x)=x^3-6x^2+11x-6

                 clearly , f(x) is a polynomial with integer coefficients and the coefficient of the highest degree term i.e. the leading coefficient is 1 .

                therefore , integer roots of f(x) are limited to the integer factorsof 6, which are pm1,pm2,pm3,pm6.

 we observe that,

                  f(1)=1-6+11-6=0    , f(2)=8-24+22-6=0      f(3)=27-54+33-6=0

          Hence ,integral roots of f(x) are 1 ,2,3.

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Deependra Verma

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