Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and then choose the correct option. I. 10x2 - 7x + 1 = 0 II. 35y2 - 12y + 1 = 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
A Correct answer
Explanation

I: 10x^2 - 7x + 1 = 0 => (2x-1)(5x-1) = 0 => x = 0.5, 0.2. II: 35y^2 - 12y + 1 = 0 => (5y-1)(7y-1) = 0 => y = 0.2, 0.1428. Comparing roots: 0.5 > 0.2, 0.5 > 0.1428, 0.2 = 0.2, 0.2 > 0.1428. Thus, x >= y.

AI explanation

Factoring equation I gives (5x - 1)(2x - 1) = 0, so the roots are x = 1/5 and x = 1/2. Factoring equation II gives (7y - 1)(5y - 1) = 0, so the roots are y = 1/7 and y = 1/5. Comparing the roots, we find that 1/5 is equal to 1/5 and 1/2 is greater than 1/7, meaning x is either equal to or greater than y in all cases.

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