Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 15x²- 11x-12=0 II. 20y²- 49y+30=0

  1. if x < y

  2. if x ≤ y

  3. if x = y or no relation can be established

  4. if x > y

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

I: 15x^2 - 11x - 12 = 0. Roots: x = (11 +/- sqrt(121 + 720))/30 = (11 +/- 29)/30. x = 40/30 = 4/3 or x = -18/30 = -3/5. II: 20y^2 - 49y + 30 = 0. Roots: y = (49 +/- sqrt(2401 - 2400))/40 = (49 +/- 1)/40. y = 50/40 = 5/4 or y = 48/40 = 6/5. Comparing: 4/3 (1.33) vs 5/4 (1.25) and 6/5 (1.2). No consistent relation.

AI explanation

Factoring equation I, 15x squared minus 11x minus 12 equals 15x squared minus 20x plus 9x minus 12, which gives the roots x = 4/3 and x = -0.6. Factoring equation II, 20y squared minus 49y plus 30 equals 20y squared minus 24y minus 25y plus 30, which gives the roots y = 1.2 and y = 1.25. Comparing the values, x = 4/3 is greater than both y values, but x = -0.6 is less than both y values, so no single relationship holds. Therefore, the relationship cannot be established.

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