Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and select the correct answer. I. 2x2 + 18x + 36 = 0 II. 2y2 - 9y + 9 = 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
C Correct answer
Explanation

Equation I: 2x^2 + 18x + 36 = 0 -> x^2 + 9x + 18 = 0 -> (x+6)(x+3) = 0, so x = -6, -3. Equation II: 2y^2 - 9y + 9 = 0 -> (2y-3)(y-3) = 0, so y = 1.5, 3. Comparing the sets, all values of x are less than all values of y.

AI explanation

Factor the first equation by dividing by 2 to get x2 + 9x + 18 = 0, which yields roots of x = -3 and x = -6. Factoring the second equation gives (2y - 3)(y - 3) = 0, so the roots for y are 1.5 and 3. Since both values of x (-3 and -6) are less than both values of y (1.5 and 3), x < y.

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