What is the solution of x^3-4x^2+x-4 = 0

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The solution of x^3-4x^2+x-4 = 0 has to be determined.

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

=> x^2(x - 4) + 1(x - 4) = 0

=> (x^2 + 1)(x - 4) = 0

x^2 + 1 = 0

=> x^2 = -1

=> x = `+-sqrt(-1)`

=> x = `+-i`

x - 4 = 0

=> x = 4

The solution of the equation x^3-4x^2+x-4 = 0 is {-i, i, 4}

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