Multiple choice

Directions: The following question is provided with two equations. You are required to solve the equations and identify the correct answer from the alternatives given below. I. x2 + 7x + 6 = 0 II. y2 + 13y + 42 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

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

Solving I: x^2 + 7x + 6 = 0 gives (x+6)(x+1) = 0, so x = -6, -1. Solving II: y^2 + 13y + 42 = 0 gives (y+6)(y+7) = 0, so y = -6, -7. Comparing values: x can be -6 or -1, y can be -6 or -7. If x=-6, y=-6 (x=y); if x=-1, y=-6 or -7 (x>y). Thus x >= y.

AI explanation

Using the method of factorization for quadratic equations, the first equation x2 + 7x + 6 = 0 factors into (x + 1)(x + 6) = 0, giving roots x = -1 and x = -6. The second equation y2 + 13y + 42 = 0 factors into (y + 6)(y + 7) = 0, giving roots y = -6 and y = -7. Comparing the values, -1 is greater than both -6 and -7, and -6 is equal to -6 but greater than -7. Therefore, x is always greater than or equal to y.

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