Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and then choose the correct option. I. 5x2 - 16x + 11 = 0 II. 5y2 - 3y – 2 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

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

I: 5x^2 - 16x + 11 = 0 -> (5x - 11)(x - 1) = 0 -> x = 1, 2.2. II: 5y^2 - 3y - 2 = 0 -> (5y + 2)(y - 1) = 0 -> y = 1, -0.4. Comparing: x=1, y=1 (x=y); x=2.2, y=-0.4 (x>y). Thus x >= y.

AI explanation

Factor the first equation 5x2 - 16x + 11 = 0 to get (5x - 11)(x - 1) = 0, so the roots are x = 11/5 and x = 1. Factor the second equation 5y2 - 3y - 2 = 0 to get (5y + 2)(y - 1) = 0, which gives the roots y = -2/5 and y = 1. Comparing the values, x is either greater than or equal to the corresponding values of y. Therefore, the relationship is x >= y.

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