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      Question

      Let 's' represent the sum of the highest root of

      equations I and III, and 'r' denote the product of the lowest root of equation I and the highest root of equation II.Determine the new equation if the roots of this equation are 's'and 'r'. Solve the three equations and construct a new equation in variable 'c' (reduced to the lowest possible factor) using roots of equations I, II, and III, following the instructions provided below.
      A x² - 14x + 40 = 0 Correct Answer Incorrect Answer
      B x² - 18x + 72 = 0 Correct Answer Incorrect Answer
      C x² - 24x + 80 = 0 Correct Answer Incorrect Answer
      D x² - 13x + 58 = 0 Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      ATQ, 4 - (20/a) + (28/a) = a2 = (4/a2) + (9/a) - 3 7 - (29/a) + (24/a2) = 0 7a2 - 29a + 24 = 0 (7a - 8)(a - 3) = 0 a = 8/7, 3 Equation II b2 - 4b + 2 = 1/8 × (2b - 5) 8b2 - 32b + 16 = 2b - 5 8b2 - 34b + 21 = 0 (4b - 3)(2b - 7) = 0 b = 3/4, 7/2 Equation III, c2 + 10.5 = 17c/2 2c2 - 17c + 21 = 0 (2c - 3)(c - 7) = 0 c = 3/2, 7 s = 3 + 7 = 10 r = (8/7) × (7/2) = 4 New Equation (x - 10)(x - 4) = 0 x2 - 14x + 40 = 0

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