Multiple choice

Directions: In the following question, there are two quadratic equations. Study both the equations carefully and answer accordingly. I. 35x2 - 17x + 2 = 0 II. 20y2 - 27y + 9 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or no relation can be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 35x^2 - 17x + 2 = 0 => (5x-1)(7x-2) = 0 => x = 0.2, 0.285. II: 20y^2 - 27y + 9 = 0 => (4y-3)(5y-3) = 0 => y = 0.75, 0.6. Comparing values, x < y.

AI explanation

Solving the first quadratic equation 35x squared minus 17x plus 2 equals 0 by factorization gives (x minus 0.2)(35x minus 10) equals 0, so x equals 0.2 or 0.28. Solving the second equation 20y squared minus 27y plus 9 equals 0 gives (y minus 0.6)(20y minus 15) equals 0, so y equals 0.6 or 0.75. Comparing the values reveals that both values of x are strictly less than both values of y, therefore x is less than y.

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