In the following question, two equations numbered I and II are given. You have to solve both the equations to establish the relationship between x and y and choose the correct option.
I. 12x² + 11x + 2 = 0
II. 15y² + 14y + 3 = 0?

From I: 12x² + 11x + 2 = 0 Or, 12x² + 8x + 3x + 2 = 0 Or, 4x(3x + 2) + 1(3x + 2) = 0 Or, (4x + 1)(3x + 2) = 0 So, x = −1/4 or x = −2/3 (i.e., x = −0.25 or −0.67) From II: 15y² + 14y + 3 = 0 Or, 15y² + 9y + 5y + 3 = 0 Or, 3y(5y + 3) + 1(5y + 3) = 0 Or, (3y + 1)(5y + 3) = 0 So, y = −1/3 or y = −3/5 (i.e., y = −0.33 or −0.60) On comparing the values of x and y: For x = −0.25 and y = −0.33, x > y For x = −0.67 and y = −0.60, x < y Therefore, relationship between x and y cannot be established. Hence, the correct answer is E.