Multiple choice

Directions: Solve the given equations and choose the appropriate answer. I. 35x2 – 29x + 6 = 0 II. 20y2 + y – 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

For 35x^2 - 29x + 6 = 0, roots are x = 6/35 and 5/35 = 1/7 or 6/35 and 1/5. Factoring gives (5x-2)(7x-3)=0, so x = 2/5 and 3/7. For 20y^2 + y - 1 = 0, (4y-1)(5y+1)=0, so y = 1/4 and -1/5. Comparing values, x > y.

AI explanation

Factor the first equation 35x2 - 29x + 6 = 0 by splitting the middle term to get (7x - 3)(5x - 2) = 0, which gives the roots x = 3/7 and x = 2/5. Factor the second equation 20y2 + y - 1 = 0 as (5y - 1)(4y + 1) = 0, yielding the roots y = 1/5 and y = -1/4. Comparing the roots, the smallest x value is 3/7 (approx. 0.428), which is greater than the largest y value of 1/5 (0.2). Consequently, x is greater than y.

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