Multiple choice

Directions: In the following question, two equations (i) and (ii) are given, you have to solve both the equations and give answer accordingly. (i) 6x2 – 17x + 7 = 0 (ii) 2y2 – 18y + 28 = 0

  1. x = y or no relation can be established between x & y.

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x > y
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A Correct answer
Explanation

i) 6x^2 - 17x + 7 = 0 -> (2x-1)(3x-7) = 0 -> x = 0.5, 2.33. ii) 2y^2 - 18y + 28 = 0 -> y^2 - 9y + 14 = 0 -> (y-2)(y-7) = 0 -> y = 2, 7. Comparing: x=0.5 < y=2, x=0.5 < y=7, x=2.33 > y=2, x=2.33 < y=7. Since x can be greater or less than y, no relation can be established.

AI explanation

Solving the first quadratic equation 6x squared minus 17x plus 7 equals 0 by factorization gives (2x minus 1)(3x minus 7) equals 0, so x equals 0.5 or 2.33. Solving the second equation 2y squared minus 18y plus 28 equals 0 gives (y minus 2)(2y minus 14) equals 0, so y equals 2 or 7. Since x can be 2.33 which is greater than y equals 2, but x can also be 0.5 which is less than y equals 2, no relation can be established between x and y.

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