Multiple choice

Directions: In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. 3x2 – 5x – 12 = 0 II. 2y2 + 15y + 25 = 0

  1. x > y

  2. x ≤ y

  3. x ≥ y

  4. x < y

  5. Either x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

I: 3x^2 - 5x - 12 = 0 => (3x+4)(x-3) = 0 => x = -4/3, 3. II: 2y^2 + 15y + 25 = 0 => (2y+5)(y+5) = 0 => y = -2.5, -5. Comparing values, x is always greater than y.

AI explanation

Use the factorization method on equation I to split the middle term of 3x^2 - 5x - 12 = 0 into -9x and 4x, yielding (3x + 4)(x - 3) = 0, which gives the roots x = -4/3 and x = 3. For equation II, use the factorization method to split the middle term of 2y^2 + 15y + 25 = 0 into 10y and 5y, yielding (2y + 5)(y + 5) = 0, meaning the roots are y = -5/2 and y = -5. Comparing the values, the smallest x is -4/3 and the largest y is -5/2, so x > y.

Keep practicing — related questions