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. 90x2 + 90x + 20 = 0 II. 36y2 – 66y + 24 = 0

  1. x < y

  2. x ≤ y

  3. x = y, or the relationship cannot be established.

  4. x ≥ y

  5. x > y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

I: 90x^2 + 90x + 20 = 0 -> 9x^2 + 9x + 2 = 0 -> (3x+1)(3x+2) = 0. x = -1/3, -2/3. II: 36y^2 - 66y + 24 = 0 -> 6y^2 - 11y + 4 = 0 -> (2y-1)(3y-4) = 0. y = 1/2, 4/3. Comparing values, x < y.

AI explanation

Factor the first equation by taking 10 common to get 10(9x squared + 9x + 2)=0, which further factors into 10(3x+1)(3x+2)=0, yielding x=-1/3 or x=-2/3. Divide the second equation by 6 to get 6y squared - 11y + 4 = 0, which factors into (3y-4)(2y-1)=0, yielding y=4/3 or y=1/2. Since both values of x are negative and both values of y are positive, x is always less than y. Therefore, x < y.

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