In the question, two Quantities I and II are given. You have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option. Which of the following pair of symbols will define the relation between Quantity I and Quantity II and between Quantity II and Quantity III respectively? A. = B. > C. 'q' > 'r'. x³- 9x²+ 23x - 15 = 0 Quantity I: Find the value of '8p'. Quantity II: Find the value of (q + 40). Quantity III: Find the value of (r X 20).

Explanation

1 Detailed solution: x³- 9x²+ 23x - 15 = 0 Or, x X (x²- 9x + 23) = 15 Or, x X (x²- 9x + 23) = 15 X 1 So, let x = 1 So, 1 X (1²- 9 X 1 + 23) = 15 Or, 1 - 9 + 23 = 15 Or, 15 = 15 Since, LHS = RHS, x = 1 So, we can divide the given equation by (x - 1). On dividing the given equation by (x - 1), we have; (x³- 9x²+ 23x - 15) = (x - 1) (x²- 8x + 15) Or, x²- 8x + 15 = 0 Or, x²- 5x - 3x + 15 = 0 Or, x(x - 5) - 3(x - 5) = 0 Or, (x - 5) (x - 3) = 0 So, x = 5 or x = 3 Since, p > q > r So, p = 5, q = 3 and r = 1 Quantity I: Required value = 8 X 5 = 40 So, Quantity I = 40 Quantity II: Required value = 3 + 40 = 43 So, Quantity II = 43 Quantity III: Required value = 1 X 20 = 20 So, Quantity III = 20 So, Quantity I Quantity III