Multiple choice

Directions: In the following question, two equations (I) and (II) are given. You have to solve both the equations and give answer as per the codes given below: I. x2 – 5x + 6 = 0 II. 2y2 – y – 3 = 0

  1. if x > y

  2. if x ≥ y

  3. if x < y

  4. if x ≤ y

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

I: x^2 - 5x + 6 = 0 => (x-2)(x-3) = 0, x = 2, 3. II: 2y^2 - y - 3 = 0 => (2y-3)(y+1) = 0, y = 1.5, -1. Comparing x values (2, 3) and y values (1.5, -1), x is always greater than y.

AI explanation

Factorizing equation one, x squared minus 5x plus 6 equals 0, yields (x - 2)(x - 3) equals 0, so the roots are x equals 3 and x equals 2. Factorizing equation two, 2y squared minus y minus 3 equals 0, gives (2y - 3)(y + 1) equals 0, which means the roots are y equals 1.5 and y equals -1. Since both values of x are strictly greater than both values of y, the established relationship is x > y.

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