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AP EAMCET202119 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

If α , β are the roots of 11 x 2 + 12 x - 13 = 0 , then 1 α 2 + 1 β 2 = ? (approximately close to)

Options

  1. A4 . 54
  2. B3 . 54
  3. C2 . 54
  4. D1 . 54

Correct answer

C. 2 . 54

Step-by-step solution

Given, 11 x 2 + 12 x - 13 = 0 Then, α + β = - 12 11 and α β = - 13 11 Now, 1 α 2 + 1 β 2 = α 2 + β 2 α 2 β 2 = α + β 2 - 2 α β α β 2 Putting the values we get, = - 12 11 2 - 2 - 13 11 - 13 11 2 = 1 . 19 + 2 . 36 1 . 39 ≈ 2 . 54

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