JEE Main202126 Feb 2021Morning ShiftMathematicsQuadratic EquationActual

The sum of 162 t h power of the roots of the equation x 3 - 2 x 2 + 2 x - 1 = 0 is ______.

Correct answer

Step-by-step solution

x 3 - 2 x 2 + 2 x - 1 = 0 x = 1 satisfying the equation ∴   x - 1 is factor of x 3 - 2 x 2 + 2 x - 1 = x - 1 x 2 - x + 1 = 0 x = 1 , 1 + i 3 2 , 1 - i 3 2 x = 1 , - ω 2 , - ω sum of 162 t h power of roots = 1 162 + - ω 2 162 + - ω 162 = 1 + ω 324 + ω 162 = 1 + 1 + 1 = 3

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