Find all the roots of x^3-4x^2+5x-2=0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation x^3-4x^2+5x-2=0 has to be solved for x.

x^3-4x^2+5x-2=0

=> x^3 - 2x^2 - 2x^2 + 4x + x - 2 = 0

=> x^2(x - 2) - 2x(x - 2) + 1(x - 2) = 0

=> (x^2 - 2x + 1)(x - 2) = 0

=> (x - 1)^2*(x - 2) = 0

x = 1 and x = 2

The solution of x^3-4x^2+5x-2=0 is x = 1 and x = 2

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