Multiple choice

Directions: In the given question, two equations numbered I and II are given. You have to solve both the equations and find out the relationship between x and y. I. 5x2 + 2x = 0 II. 6y2 - 5y + 1 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 5x^2 + 2x = 0 => x(5x + 2) = 0, so x = 0 or x = -0.4. II: 6y^2 - 5y + 1 = 0 => (2y - 1)(3y - 1) = 0, so y = 0.5 or y = 0.33. Comparing values: 0 < 0.33, 0 < 0.5, -0.4 < 0.33, -0.4 < 0.5. Thus, x < y.

AI explanation

Factor the first equation x(5x + 2) = 0 to find the roots x = 0 and x = -2/5. Factor the second quadratic 6y2 - 5y + 1 = 0 to get (3y - 1)(2y - 1) = 0, giving the roots y = 1/3 and y = 1/2. Both values of x are negative or zero, while both values of y are positive. Therefore, x is strictly less than y.

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