Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and choose the correct option. I: 6x2 - 13x + 6 = 0 II: 4y2 - 20y + 24 = 0

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or the relationship cannot be established.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 6x^2 - 13x + 6 = 0 => (2x-3)(3x-2) = 0 => x = 1.5, 0.66. II: 4y^2 - 20y + 24 = 0 => y^2 - 5y + 6 = 0 => (y-2)(y-3) = 0 => y = 2, 3. Comparing, all values of x are less than all values of y.

AI explanation

For equation I, factor 6x squared minus 13x plus 6 equals 0 to find the roots are x equals 3/2 and x equals 2/3. For equation II, factor 4y squared minus 20y plus 24 equals 0 to find the roots are y equals 2 and y equals 3. Comparing these values, both possible values of x are smaller than the smallest possible value of y. Therefore, x is always less than y.

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