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JEE Main202229 Jun 2022Evening ShiftMathematicsQuadratic EquationActual

Let α be a root of the equation 1 + x 2 + x 4 = 0 . Then the value of α 1011 + α 2022 - α 3033 is equal to:

Options

  1. A1
  2. Bα
  3. C1 + α
  4. D1 + 2 α

Correct answer

A. 1

Step-by-step solution

Given, x 4 + x 2 + 1 = 0 Using the formula a 4 + a 2 + 1 = a 2 + a + 1 a 2 - a + 1 We get, x 2 + x + 1 x 2 - x + 1 = 0 ⇒ x = ± ω ,   ± ω 2 where ω = 1 1 / 3 and imaginary. So α 1011 + α 2022 - α 3033 = 1 + 1 - 1 = 1

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