Multiple choice

Directions: In this question, two equations numbered I and II are given. You have to solve both the equations and choose the correct option accordingly. I. x2 - 10x + 24 = 0 II. y2 - 14y + 48 = 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 - 10x + 24 = 0 gives (x-6)(x-4)=0, so x=6 or 4. Solving II: y^2 - 14y + 48 = 0 gives (y-8)(y-6)=0, so y=8 or 6. Comparing the sets {4, 6} and {6, 8}, we see x is always <= y.

AI explanation

Factoring the first equation x^2 - 10x + 24 = 0 gives (x - 4)(x - 6) = 0, so x = 4 or x = 6. Factoring the second equation y^2 - 14y + 48 = 0 gives (y - 6)(y - 8) = 0, so y = 6 or y = 8. Comparing the roots, x is less than or equal to y in all cases, meaning x <= y.

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