Multiple choice

Directions: There are two equations given in the problem. Solve the equations and answer accordingly. I. 3x2 + 11x + 10 = 0 II. 2y2 + 13y + 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
A Correct answer
Explanation

Solving 3x^2 + 11x + 10 = 0 gives (3x + 5)(x + 2) = 0, so x = -5/3 or -2. Solving 2y^2 + 13y + 21 = 0 gives (2y + 7)(y + 3) = 0, so y = -3.5 or -3. Comparing the values, -5/3 (-1.67) and -2 are both greater than -3.5 and -3, so x > y.

AI explanation

Factoring the first equation by splitting the middle term results in 3x^2 + 6x + 5x + 10 = 0, giving (3x + 5)(x + 2) = 0 and roots x = -5/3 and x = -2. Factoring the second equation gives 2y^2 + 6y + 7y + 21 = 0, leading to (2y + 7)(y + 3) = 0 and roots y = -7/2 and y = -3. Since both values of x are greater than both values of y, x > y.

Keep practicing — related questions