Multiple choice

Directions: In this question, two equations are given, numbered I and II. You have to solve both the equations and compare the two quantities. Choose the correct option accordingly. I. x2 - 9x + 18 = 0 II. y2 - 5y + 6 = 0

  1. x < y

  2. x ≥ y

  3. x > y

  4. x ≤ y

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

Solving I: x^2 - 9x + 18 = 0 gives (x-3)(x-6)=0, so x=3, 6. Solving II: y^2 - 5y + 6 = 0 gives (y-2)(y-3)=0, so y=2, 3. Comparing the sets {3, 6} and {2, 3}, we see that for any x and y, x >= y is always true.

AI explanation

Factor the first equation using the splitting the middle term method to get (x-3)(x-6)=0, yielding x=3 or x=6. Factor the second equation to get (y-2)(y-3)=0, yielding y=2 or y=3. Since 6 is greater than both 2 and 3, and 3 is equal to 3 and greater than 2, every value of x is greater than or equal to every value of y. Therefore, x >= y.

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