Multiple choice

In each of the following questions, two equations are given. You have to solve them and Give answer. ( (I) ) (105x^2 + 593x + 186 = 0 ) ( (II) ) ( 69y^2 - 107y - 126 = 0 )

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or relationship cannot be established

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For equation (I): 105x² + 593x + 186 = 0. Using the quadratic formula: x = [-593 ± √(593² - 4×105×186)]/(2×105) = [-593 ± √(351649 - 78120)]/210 = [-593 ± √273529]/210 = [-593 ± 523]/210, giving x = -70/210 = -1/3 or x = -1116/210 = -5.31. For equation (II): 69y² - 107y - 126 = 0. Using the quadratic formula: y = [107 ± √(11449 - 4×69×(-126))]/(2×69) = [107 ± √(11449 + 34776)]/138 = [107 ± √46225]/138 = [107 ± 215]/138, giving y = 322/138 = 2.33 or y = -108/138 = -0.78. Comparing: x = -1/3 > y = -0.78, but x = -5.31 < y = 2.33. Since the relationship between x and y is not consistent, the relationship cannot be established.