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JEE Main20265 April 2026Morning ShiftMathematicsQuadratic EquationActual

Let a, b C . Let , be the roots of the equation x^2 + ax + b = 0 . If - = 11 and ^2 - ^2 = 3i 11 , then ( ^3 - ^3)^2 is equal to:

Options

  1. A160
  2. B176
  3. C194
  4. D187

Correct answer

B. 176

Step-by-step solution

Given - = 11 and ^2 - ^2 = 3i 11 + = ^2 - ^2 - = 3i 11 11 = 3i Using the identity ( - )^2 = ( + )^2 - 4 ( 11 )^2 = (3i)^2 - 4 11 = -9 - 4 4 = -20 = -5 Now, ^3 - ^3 = ( - )( ^2 + + ^2) ^3 - ^3 = ( - )(( + )^2 - ) ^3 - ^3 = 11 ((3i)^2 - (-5)) ^3 - ^3 = 11 (-9 + 5) = -4 11 Squaring both sides, we get: ( ^3 - ^3)^2 = (-4 11 )^2 = 16 11 = 176 Answer: 176

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