Multiple choice

Directions: In the following question, two equations are given. You have to solve both the equations and choose the correct relationship accordingly. I. 27x2 + 30x + 8 = 0 II.3y2 + 5y + 2 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

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

I. 27x^2 + 30x + 8 = 0. Roots: x = (-30 +/- sqrt(900 - 864)) / 54 = (-30 +/- 6) / 54. x1 = -24/54 = -0.44, x2 = -36/54 = -0.66. II. 3y^2 + 5y + 2 = 0. (3y+2)(y+1) = 0. y1 = -2/3 = -0.66, y2 = -1. Comparing, x >= y.

AI explanation

Factoring the first equation 27x^2 + 30x + 8 = 0 by splitting the middle term gives 27x^2 + 18x + 12x + 8 = 0, which groups into (3x + 2)(9x + 4) = 0, so x = -2/3 and x = -4/9. Applying the same method to the second equation 3y^2 + 5y + 2 = 0 gives 3y^2 + 3y + 2y + 2 = 0, which factors into (3y + 2)(y + 1) = 0, yielding y = -2/3 and y = -1. Since the maximum value of x is -4/9 and the maximum value of y is -2/3, the root -4/9 is greater than both y values, but the root -2/3 is equal to y; therefore, the combined relationship is x ≥ y.

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