Multiple choice

In the following questions two equations numbered I and II are given. You have to solve both the equations and choose the correct option. I. x2-15x +36 = 0 II. 10y2 +31y -63 = 0

  1. x < y

  2. x > y

  3. x ≤ y

  4. x ≥ y

  5. x = y or relationship cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving I: x^2 - 15x + 36 = 0 gives (x-3)(x-12) = 0, so x = 3, 12. Solving II: 10y^2 + 31y - 63 = 0, using the quadratic formula or factoring, gives (2y + 9)(5y - 7) = 0, so y = -4.5, 1.4. Comparing the sets, all values of x are greater than all values of y.

AI explanation

Factoring equation one gives (x - 12)(x - 3) = 0, so x = 12 or x = 3. Factoring equation two gives (5y - 9)(2y + 7) = 0, so y = 1.8 or y = -3.5. Since 3 is greater than both 1.8 and -3.5, and 12 is also greater than both y values, x > y.

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