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. I. x2 - 26x + 165 = 0 II. y2 - 16y = -63

  1. if x > y

  2. if x ≥ y

  3. if x < y

  4. if x ≤ y

  5. if x = y or or relation cannot be established
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A Correct answer
Explanation

I: x^2 - 26x + 165 = 0 -> (x-11)(x-15) = 0, x = 11, 15. II: y^2 - 16y + 63 = 0 -> (y-7)(y-9) = 0, y = 7, 9. Since all x values (11, 15) are greater than all y values (7, 9), x > y.

AI explanation

Factoring equation I, x^2 - 26x + 165 = 0, we find two numbers that multiply to 165 and add to 26, giving the factors (x - 11)(x - 15) = 0 and roots x = 11 and x = 15. For equation II, y^2 - 16y + 63 = 0 factors into (y - 7)(y - 9) = 0, yielding roots y = 7 and y = 9. Comparing the roots, both values of x are greater than both values of y. Therefore, the relationship is x > y.

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