Multiple choice

Directions: In the question, two equations numbered I and II are given. You have to solve both the equations and give the answer. I. x2 + 18x + 81 = 0 II. y2 + 14y + 49 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or relationship cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Equation I: x^2 + 18x + 81 = 0 factors to (x+9)^2 = 0, so x = -9. Equation II: y^2 + 14y + 49 = 0 factors to (y+7)^2 = 0, so y = -7. Since -9 < -7, x < y.

AI explanation

The first equation is a perfect square trinomial, (x + 9)^2 = 0, giving the single root x = -9. The second equation is also a perfect square trinomial, (y + 7)^2 = 0, resulting in y = -7. Comparing these values on the number line, -9 is strictly less than -7, which shows that x < y.

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