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. x2 + 5x + 6 = 0 II. 11y2 + 18y + 7 = 0

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y, or the relationship cannot be established.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: x^2 + 5x + 6 = 0 => (x+2)(x+3) = 0 => x = -2, -3. II: 11y^2 + 18y + 7 = 0 => (11y+7)(y+1) = 0 => y = -7/11 (~ -0.63), -1. Since -2 < -1 and -3 < -0.63, x < y.

AI explanation

Factoring equation I, x^2 + 5x + 6 = 0, gives (x + 3)(x + 2) = 0, so x = -3 and x = -2. Factoring equation II, 11y^2 + 18y + 7 = 0, by splitting the middle term gives 11y^2 + 11y + 7y + 7 = 0, which factors into (11y + 7)(y + 1) = 0, so y = -7/11 and y = -1. Comparing the values, both roots of x (-3 and -2) are smaller than both roots of y (-7/11 and -1), which means x < y.

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