Multiple choice

Directions: There are two equations given in the problem. Solve the equations and answer accordingly. I. x2 - 22x + 117 = 0 II. 2y2 + y - 120 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or no relation can be established
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A Correct answer
Explanation

For x^2 - 22x + 117 = 0, the roots are (x-9)(x-13)=0, so x = 9, 13. For 2y^2 + y - 120 = 0, using the quadratic formula, y = (-1 +/- sqrt(1 + 960)) / 4 = (-1 +/- 31) / 4, giving y = 7.5 or -8. Comparing the sets {9, 13} and {7.5, -8}, all values of x are greater than all values of y.

AI explanation

Factoring equation I gives (x - 13)(x - 9) = 0, yielding x = 13 or x = 9. Factoring equation II gives (2y - 15)(y + 8) = 0, yielding y = 7.5 or y = -8. Since both values of x are larger than both values of y, the relationship is x > y.

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