Multiple choice

In each of the following questions, two equations are given. You have to solve them and answer the question. (I) (2x^2 + 17x + 30 = 0) (II) (4y^2 – 13y – 12 = 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
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A Correct answer
Explanation

Factorizing equation (I): 2x² + 17x + 30 = (2x + 5)(x + 6) = 0, so x = -5/2 = -2.5 or x = -6. Factorizing equation (II): 4y² - 13y - 12 = (4y + 3)(y - 4) = 0, so y = -3/4 = -0.75 or y = 4. Comparing values: when x = -2.5, both y values (-0.75, 4) are greater. When x = -6, both y values (-0.75, 4) are greater. Therefore x < y for all combinations.

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