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. 15x2 + 14x + 3 = 0 II. 15y2 - y - 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
D Correct answer
Explanation

Solving 15x^2 + 14x + 3 = 0: (3x+1)(5x+3) = 0, so x = -1/3, -3/5. Solving 15y^2 - y - 2 = 0: (3y+1)(5y-2) = 0, so y = -1/3, 2/5. Comparing: -1/3 = -1/3, -1/3 < 2/5, -3/5 < -1/3, -3/5 < 2/5. Thus, x <= y.

AI explanation

Factor the first equation by splitting the middle term to get (3x + 1)(5x + 3) = 0, giving the roots x = -1/3 and x = -3/5. For the second equation, factoring gives (3y - 2)(5y + 1) = 0, resulting in the roots y = 2/3 and y = -1/5. When comparing the values, one x root is smaller than a y root while the other equals a y root, establishing that x is less than or equal to y.

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