Multiple choice

Directions: In the following question, two equations numbered (I) and (II) are given. Student should solve both the equations and mark appropriate answer. I. 4x2 - 16x + 7 = 0 II. 5y2 - 14y + 8 = 0

  1. If x > y

  2. If x = y or no relation can be established

  3. If x < y

  4. If x ≥ y

  5. If x ≤ y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 4x^2 - 16x + 7 = 0. Roots: (16 +/- sqrt(256 - 112))/8 = (16 +/- 12)/8. x = 28/8 = 3.5 or x = 4/8 = 0.5. II: 5y^2 - 14y + 8 = 0. Roots: (14 +/- sqrt(196 - 160))/10 = (14 +/- 6)/10. y = 20/10 = 2 or y = 8/10 = 0.8. Comparing: x=3.5 > y=2, but x=0.5 < y=0.8. No relation.

AI explanation

Solving the first quadratic equation 4x squared minus 16x plus 7 equals 0 by splitting the middle term gives (2x minus 1)(2x minus 7) equals 0, so x equals 0.5 or 3.5. Solving the second equation 5y squared minus 14y plus 8 equals 0 gives (y minus 2)(5y minus 4) equals 0, so y equals 2 or 0.8. Since x can be 0.5 which is less than y equals 0.8, but x can also be 3.5 which is greater than y equals 2, no relation can be established between x and y.

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