Multiple choice

In the following questions, two equations (x) and (y) are given. You have to solve both the equations and give answer. (I.) (2x^2 - x - 66 = 0) (II.) (3y^2 - 5y - 42 = 0)

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or the relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Equation I: 2x² - x - 66 = 0. Factoring: (2x + 11)(x - 6) = 0, so x = -5.5 or x = 6. Equation II: 3y² - 5y - 42 = 0. Factoring: (3y + 7)(y - 6) = 0, so y = -7/3 ≈ -2.33 or y = 6. When x = 6, y = 6, we have x = y. When x = 6, y = -2.33, we have x > y. When x = -5.5, y = 6, we have x < y. When x = -5.5, y = -2.33, we have x < y. Since the relationship varies (sometimes x > y, sometimes x < y, sometimes x = y), the correct answer is 'the relation cannot be established'.

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