Multiple choice

Directions: In the problem, two equations numbered I and II are given. You have to find the relationship between them by solving both the equations and then mark the answer accordingly. I. x2 + 8x + 15 = 0 II. y2 - 14y + 45 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or if there is no relation between 'x' and 'y'.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: x^2 + 8x + 15 = 0 -> (x+3)(x+5) = 0 -> x = -3, -5. II: y^2 - 14y + 45 = 0 -> (y-5)(y-9) = 0 -> y = 5, 9. Clearly, all values of x are less than all values of y.

AI explanation

Using the method of factorization, the first equation becomes (x + 3)(x + 5) = 0, which gives x = -3 and x = -5. The second equation factors to (y - 5)(y - 9) = 0, so y = 5 or y = 9. Comparing these values, both roots of x are negative while both roots of y are positive, meaning every value of x is strictly less than every value of y. Therefore, the relationship is x < y.

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