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 - 1 + x = 0 (II) 7y + 2 = 22y2

  1. x > y

  2. x < y

  3. x = y or no relationship can be established between 'x' and 'y'

  4. x ≤ y

  5. x ≥ y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Equation I: 2x^2 + x - 1 = 0 factors to (2x - 1)(x + 1) = 0, so x = 0.5 or -1. Equation II: 22y^2 - 7y - 2 = 0 factors to (11y + 2)(2y - 1) = 0, so y = -2/11 or 0.5. Comparing these values, x can be greater than, less than, or equal to y depending on the specific roots chosen, so no unique relationship exists.

AI explanation

Factoring the first equation 2x2 + x - 1 = 0 gives (2x - 1)(x + 1) = 0, yielding roots x = 1/2 and x = -1. Factoring the second equation 22y2 - 7y - 2 = 0 gives (11y + 2)(2y - 1) = 0, yielding roots y = 1/2 and y = -2/11. When comparing the values, x = 1/2 is equal to y = 1/2, x = -1 is less than both y values, and x = 1/2 is greater than y = -2/11. Since there is no consistent inequality, no relationship can be established.

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