Multiple choice

In each of the following question, two equation (I) and (II) is given. You have to solve them and answer the question.( (I) 4x^2 + 51x + 135 = 0 ) ( (II) 2y^2 + 11y + 15 = 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
A Correct answer
Explanation

Solve equation (I): 4x² + 51x + 135 = 0 factors to (x + 12)(4x + 11.25) = 0 (checking: 4 × 11.25 = 45, not 135). Let's use quadratic formula or re-factor: (4x + 15)(x + 9) = 4x² + 51x + 135. So x = -15/4 = -3.75 or x = -9. Solve equation (II): 2y² + 11y + 15 = 0 factors to (2y + 5)(y + 3) = 0. So y = -5/2 = -2.5 or y = -3. Compare: when x = -9 and y = -2.5, we have x < y. When x = -3.75 and y = -3, we have x < y. Thus x < y, confirming option A.

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