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AP EAMCET202119 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

The sum of the roots of the equation e 4 t - 10 e 3 t + 29 e 2 t - 22 e t + 4 = 0 is

Options

  1. Alog e ⁡ 10
  2. B2 log e ⁡ 2
  3. Clog 2 ⁡ 29
  4. D2 log 10 ⁡ 2

Correct answer

B. 2 log e ⁡ 2

Step-by-step solution

Let x = e t ⇒ t = log e x Then, the given equation reduces to x 4 - 10 x 3 + 29 x 2 - 22 x + 4 = 0 Now, product of roots taken all at a time of a biquadratic equation is constant   term coefficient   of   x 2 . Let x 1 ,   x 2 ,   x 3 and x 4 are the four roots of x 4 - 10 x 3 + 29 x 2 - 22 x + 4 = 0 , then x 1 x 2 x 3 x 4 = 4 1 = 4 . Taking log both sides, we get log e x 1 x 2 x 3 x 4 = log e 4 ⇒ log e x 1 + log e x 2 + log e x 3 + log e x 4 = 2 log e 2 ⇒ t 1 + t 2 + t 3

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