Multiple choice

The roots of the equation x3 - 3x2 + 2x = 0 are

  1. 1 and 2

  2. 0 and 1

  3. 0, 1 and 2

  4. 1, 2 and 3
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C Correct answer
Explanation

Factor the equation: x(x^2 - 3x + 2) = 0, which is x(x-1)(x-2) = 0. The roots are 0, 1, and 2.

AI explanation

The given equation is x^3 - 3x^2 + 2x = 0, and we first take x as a common factor to get x(x^2 - 3x + 2) = 0. This gives one root as x = 0, and then we factor the quadratic part as (x - 1)(x - 2) = 0. Setting these factors to zero yields the remaining roots x = 1 and x = 2, making the complete set of roots 0, 1 and 2.

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