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      Question

      In the questions, two equations I and II are given. You

      have to solve both the equations to establish the correct relation between x and y and choose the correct option. I. x² - (3n - 6)x + mn = 0 II. y² - ny - 45 = 20m The roots of the equation I are 'm' and 'n' and (m - n = 6). If the smallest root of equation II is 'p', then find the value of (7n + 4p).
      A 20 Correct Answer Incorrect Answer
      B 24 Correct Answer Incorrect Answer
      C 28 Correct Answer Incorrect Answer
      D 32 Correct Answer Incorrect Answer
      E 36 Correct Answer Incorrect Answer

      Solution

      m - n = 6 m = n + 6 ----------------(i) I. x² - (3n - 6)x + mn = 0 Sum of roots = (3n - 6) m + n = 3n - 6 (n + 6) + n = 3n - 6 2n + 6 = 3n - 6 3n - 2n = 6 + 6 'n' = 12 So, 'm' = 12 + 6 = 18 II. y² - ny - 45 = 20m y² - 12y - 45 = 20 X 18 y² - 12y - 45 = 360 y² - 12y - 405 = 0 y² - 27y + 15y - 405 = 0 y(y - 27) + 15(y - 27) = 0 (y - 27) (y + 15) = 0 'y' = 27 or -15 So, 'p' = -15 Required value = (7n + 4p) = 7 X 12 + 4 X (-15) = 24

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