Multiple choice

Directions: From the given equations numbered I and II, determine the relationship between x and y. I. 12x2 – 28x + 15 = 0 II. 4y2 – 20y + 21 = 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
D Correct answer
Explanation

Solving 12x^2 - 28x + 15 = 0 gives roots x = 1.5 and x = 0.833. Solving 4y^2 - 20y + 21 = 0 gives roots y = 3.5 and y = 1.5. Comparing these, x <= y holds true in all combinations.

AI explanation

Factoring the first equation by splitting the middle term gives 12x^2 - 18x - 10x + 15 = 0, leading to (6x - 5)(2x - 3) = 0 and roots x = 5/6 and x = 3/2. Factoring the second equation similarly yields 4y^2 - 14y - 6y + 21 = 0, leading to (2y - 3)(2y - 7) = 0 and roots y = 3/2 and y = 7/2. Since the maximum value of x is 3/2 and the minimum value of y is also 3/2, all values of x are either smaller than or equal to the values of y.

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