Multiple choice

Directions: In the given question, two equations numbered I and II are given. You have to solve both the equations and find the relationship between x and y. I. x2 + 7x + 12 = 0 II. y2 + 6y + 8 = 0

  1. x < y

  2. x = y or the relationship cannot be established

  3. x > y

  4. x ≥ y

  5. x ≤ y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: x^2 + 7x + 12 = 0 => (x+3)(x+4) = 0 => x = -3, -4. II: y^2 + 6y + 8 = 0 => (y+2)(y+4) = 0 => y = -2, -4. Comparing values: -3 > -4, -3 < -2, -4 = -4. Since x can be greater than, less than, or equal to y, the relationship cannot be established.

AI explanation

Factoring equation I using the product-sum method gives (x + 3)(x + 4) = 0, so x = -3 or x = -4. Factoring equation II gives (y + 2)(y + 4) = 0, so y = -2 or y = -4. When x = -3, it is less than y = -2 but greater than y = -4, meaning no single relationship can be established.

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