Multiple choice

In the following questions, two equations I and II are given. You have to solve both the equations and give answer. I: (x^2 - 19x + 78 = 0) II: (y^2 + 14y - 51 = 0)

  1. X > Y

  2. X ≥ Y

  3. X < Y

  4. X ≤ Y

  5. X = Y or the relation cannot be established
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A Correct answer
Explanation

Equation I: x² - 19x + 78 = 0 factors to (x - 6)(x - 13) = 0, so x = 6 or 13. Equation II: y² + 14y - 51 = 0 factors to (y + 17)(y - 3) = 0, so y = 3 or -17. Comparing: if x = 6, it's > both y values; if x = 13, it's also > both y values. Therefore X > Y is always true.

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