Multiple choice

Directions: In this question, two equations numbered I and II are given. You have to solve both the equations and mark the correct answer. (I) 2x2 = -3x - 1 (II) 61y2 = 123y - 2

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or no relationship can be established between 'x' and 'y'
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Equation I: 2x^2 + 3x + 1 = 0 factors to (2x + 1)(x + 1) = 0, so x = -0.5 or -1. Equation II: 61y^2 - 123y + 2 = 0. Using the quadratic formula, y = (123 +/- sqrt(123^2 - 4 * 61 * 2)) / (2 * 61) = (123 +/- sqrt(15129 - 488)) / 122 = (123 +/- sqrt(14641)) / 122 = (123 +/- 121) / 122. Thus y = 244/122 = 2 or y = 2/122 = 1/61. Comparing values, x is always less than y.

AI explanation

Rearranging the first equation gives 2x2 + 3x + 1 = 0, which factors into (2x + 1)(x + 1) = 0 to yield roots x = -1/2 and x = -1. Factoring the second equation 61y2 - 123y + 2 = 0 gives roots y = 2 and y = 1/61. Comparing these values, both roots of y are positive while both roots of x are negative. Therefore, x is always less than y.

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