Multiple choice

In each of the following questions, two equations are given. You have to solve them and answer the question. (I) (4x^2 – 9x – 9 = 0) (II) (2y^2 – 17y + 21 = 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

Factorizing equation (I): 4x² - 9x - 9 = (4x + 3)(x - 3) = 0, so x = -3/4 = -0.75 or x = 3. Factorizing equation (II): 2y² - 17y + 21 = (2y - 3)(y - 7) = 0, so y = 3/2 = 1.5 or y = 7. Comparing values: when x = -0.75, both y values (1.5, 7) are greater. When x = 3, both y values (1.5, 7) are greater. Wait - x = 3 and y = 1.5 means x > y! Let me recheck: 3 > 1.5 is true, so relationship cannot be established because sometimes x < y and sometimes x > y.