Multiple choice

Directions: In the following question, equations numbered I and II are given. You have to solve both the equations and mark the correct option. I. x2 - 22x + 120 = 0 II. y2 - 26y + 168 = 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
B Correct answer
Explanation

Eq I: x^2 - 22x + 120 = 0 -> (x-10)(x-12) = 0 -> x = 10, 12. Eq II: y^2 - 26y + 168 = 0 -> (y-12)(y-14) = 0 -> y = 12, 14. Comparing roots: 10 < 12, 10 < 14, 12 = 12, 12 < 14. Thus x <= y.

AI explanation

Using the method of factorization, the first quadratic equation factors into (x - 10) and (x - 12) = 0, yielding the roots x = 10 or 12. The second equation factors into (y - 12) and (y - 14) = 0, yielding the roots y = 12 or 14. When comparing these sets of values, 10 is strictly less than both 12 and 14, while 12 is less than 14 but equal to 12, so the relationship x ≤ y holds.

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