Multiple choice

In the following questions, two equations I and II are given. You have to solve both the equations and give answer. (I: 35x^2 - 3x - 2 = 0 ) (II: 49y^2 + 7y - 6 = 0)

  1. X > Y

  2. X ≥ Y

  3. X < Y

  4. X ≤ Y

  5. X = Y or the relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Equation I: 35x² - 3x - 2 = 0. Using quadratic formula: x = (3 ± √(9 + 280))/70 = (3 ± √289)/70 = (3 ± 17)/70. So x = 20/70 = 2/7 ≈ 0.286 or x = -14/70 = -1/5 = -0.2. Equation II: 49y² + 7y - 6 = 0 gives y = (-7 ± √(49 + 1176))/98 = (-7 ± √1225)/98 = (-7 ± 35)/98. So y = 28/98 = 2/7 ≈ 0.286 or y = -42/98 = -3/7 ≈ -0.429. The ranges overlap: x ∈ [-0.2, 0.286], y ∈ [-0.429, 0.286]. Since x can equal y (2/7), but not always be greater or less, the relationship cannot be established.

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