Multiple choice

Directions: Solve each equation and choose the correct option. I. 11x2 + 9x - 2 = 0 II. 3y2 - 7y + 4 = 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
C Correct answer
Explanation

For I: 11x^2 + 9x - 2 = 0, (11x - 2)(x + 1) = 0, so x = 2/11 or x = -1. For II: 3y^2 - 7y + 4 = 0, (3y - 4)(y - 1) = 0, so y = 4/3 or y = 1. Comparing values: 2/11 < 1 and -1 < 1, so x < y.

AI explanation

Factoring equation I gives 11x^2 + 11x - 2x - 2 = 0, so 11x(x + 1) - 2(x + 1) = 0, yielding roots x = -1 or x = 2/11. Factoring equation II gives 3y^2 - 3y - 4y + 4 = 0, so 3y(y - 1) - 4(y - 1) = 0, yielding roots y = 1 or y = 4/3. Comparing the values, both roots of y are greater than both roots of x, establishing the relationship x < y.

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