Multiple choice

Directions: There are two equations given in the problem. Solve the equations and answer accordingly. I. x2 + 5x + 6 = 0 II. y2 + 7y + 12 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

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

I: x^2 + 5x + 6 = 0 => (x+2)(x+3) = 0 => x = -2, -3. II: y^2 + 7y + 12 = 0 => (y+3)(y+4) = 0 => y = -3, -4. Comparing values: -2 > -3, -2 > -4, -3 = -3, -3 > -4. Thus x >= y.

AI explanation

Factoring the first equation x2 + 5x + 6 = 0 gives (x + 2)(x + 3) = 0, so x is -2 or -3. Factoring the second equation y2 + 7y + 12 = 0 gives (y + 3)(y + 4) = 0, so y is -3 or -4. Comparing the roots, both values of x are greater than or equal to both values of y. Therefore, the relationship is x >= y.

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