Multiple choice

Directions: In the following question, there are two quadratic equations. Study both the equations carefully and answer accordingly. I. 9x2 - 31x + 26 = 0 II. 5y2 - 12y + 7 = 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 9x^2 - 31x + 26 = 0, roots are x = (31 +/- sqrt(961 - 936)) / 18 = (31 +/- 5) / 18, so x = 2 or 13/9 (approx 1.44). For 5y^2 - 12y + 7 = 0, roots are y = (12 +/- sqrt(144 - 140)) / 10 = (12 +/- 2) / 10, so y = 1.4 or 1. Comparing values, x > y.

AI explanation

Solving the first quadratic equation 9x squared minus 31x plus 26 equals 0 by factorization gives (x minus 2)(9x minus 13) equals 0, so x equals 2 or 1.44. Solving the second equation 5y squared minus 12y plus 7 equals 0 gives (y minus 1)(5y minus 7) equals 0, so y equals 1 or 1.4. Comparing all values shows both values of x (2 and 1.44) are strictly greater than both values of y (1 and 1.4), therefore x is greater than y.

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