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) 7x = 5 + 2x2 (II) 53y - 22y2 + 5 = 0

  1. x > y

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

  3. x ≥ y

  4. x ≤ y

  5. x < y
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 2x^2 - 7x + 5 = 0 => (2x-5)(x-1) = 0 => x = 2.5, 1. II: 22y^2 - 53y - 5 = 0. Roots using quadratic formula: (53 +/- sqrt(2809 + 440))/44 = (53 +/- 57)/44. y = 110/44 = 2.5 or y = -4/44 = -0.09. Since x can be 2.5 and y can be 2.5, or x can be 1 and y can be -0.09, no relationship is established.

AI explanation

Factoring the first equation 2x2 - 7x + 5 = 0 gives (x - 1)(2x - 5) = 0, yielding roots x = 1 and x = 5/2. Factoring the second equation 22y2 - 53y - 5 = 0 gives (11y + 1)(2y - 5) = 0, yielding roots y = 5/2 and y = -1/11. Comparing the values, x = 1 is greater than y = -1/11 but less than y = 5/2, meaning no consistent inequality holds. Therefore, no relationship can be established.

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