Multiple choice

Directions: In the following question, equations (I) and (II) are given. You have to solve these equations and choose the correct option. I. 20x2 – 130x = –200 II. 9y2 + 6y + 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

Equation I: 20x^2 - 130x + 200 = 0 -> 2x^2 - 13x + 20 = 0. Roots are x = 4 and x = 2.5. Equation II: 9y^2 + 6y + 1 = 0 -> (3y+1)^2 = 0. Root is y = -1/3. Since 4 > -1/3 and 2.5 > -1/3, x > y.

AI explanation

By applying the factorization method to the first equation, we rearrange it to 20x2 - 130x + 200 = 0 and factor it as (x - 5) and (20x - 40) = 0, which gives the roots x = 5 and x = 2. Using the perfect square identity, the second equation is written as (3y + 1)2 = 0, yielding the single repeated root y = -1/3. Since both possible values of x (2 and 5) are strictly greater than the value of y (-1/3), the conclusion is that x > y.

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