Multiple choice

In each of the following questions two equations are given. Solve these equations and give answer:( (I) x^{2} - 5x - 84 =0 ) ( (II) 19y^{2}-57y+38=0 )

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. If x = y or no relationship can be established between x and y.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving equation (I): x² - 5x - 84 = 0 factors to (x - 12)(x + 7) = 0, so x = 12 or x = -7. Solving equation (II): 19y² - 57y + 38 = 0. The discriminant is 57² - 4(19)(38) = 3249 - 2888 = 361 = 19². Using quadratic formula: y = (57 ± 19)/38, giving y = 76/38 = 2 or y = 38/38 = 1. Comparing values: 12 > 2 and 12 > 1, but -7 < 2 and -7 < 1. Since x can be greater or less than y depending on which root you pick, no consistent relationship exists.

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