Multiple choice

Directions: In the following question, two equations numbered I and II are given. Solve both the equations and determine the relationship between x and y. Choose the correct option accordingly. I. x2 + 12x + 32 = 0 II. y2 + 17y + 72 = 0

  1. x < y

  2. x ≤ y

  3. x > y

  4. x ≥ y

  5. x = y or the relationship cannot be determined.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Equation I: x^2 + 12x + 32 = 0 factors to (x+8)(x+4) = 0, so x = -8, -4. Equation II: y^2 + 17y + 72 = 0 factors to (y+8)(y+9) = 0, so y = -8, -9. Comparing the values, x is always greater than or equal to y (e.g., -4 > -8, -4 > -9, -8 = -8, -8 > -9).

AI explanation

Using factorization, the first equation becomes (x + 4)(x + 8) = 0, so x equals -4 or -8. The second equation factors to (y + 8)(y + 9) = 0, giving y as -8 or -9. Since -4 is greater than both -8 and -9, and -8 is equal to -8 but greater than -9, every value of x is greater than or equal to y. Thus, the established relationship is x >= y.

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