Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer according to these codes: (a) If x > y (b) If x ≥ y (c) If x 2 - 28x + 192 = 0 II. y2 + 14y - 95 = 0

  1. (a)

  2. (b)

  3. (c)

  4. (d)

  5. (e)
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A Correct answer
Explanation

The first equation factors as (x - 12)(x - 16) = 0, so x is 12 or 16. The second equation factors as (y - 5)(y + 19) = 0, so y is 5 or -19. Every possible x is greater than every possible y, hence x > y.

AI explanation

Solving the first quadratic equation by factorization, we split the middle term to get x^2 - 16x - 12x + 192 = 0, which gives the roots x = 16 and x = 12. For the second equation, y^2 + 19y - 5y - 95 = 0 gives the roots y = -19 and y = 5. Since both values of x (12 and 16) are greater than both values of y (-19 and 5), the relationship is x > y.

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