Multiple choice

Directions: Solve the equations given below and choose the correct option. I. x2 + 4x + 4 = 0 II. y2 - 8y + 16 = 0

  1. x ≥ y

  2. x > y

  3. x ≤ y

  4. x < y

  5. x = y or no relation can be established between x and y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Equation I: x^2 + 4x + 4 = 0 implies (x+2)^2 = 0, so x = -2. Equation II: y^2 - 8y + 16 = 0 implies (y-4)^2 = 0, so y = 4. Since -2 < 4, x < y.

AI explanation

The first equation x squared plus 4x plus 4 equals zero is a perfect square trinomial, yielding the repeated root x equals negative 2. The second equation y squared minus 8y plus 16 equals zero is also a perfect square trinomial, yielding the repeated root y equals 4. Comparing these distinct roots, negative 2 is strictly less than 4, establishing that x is less than y.

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