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. 2x2 + 5x + 2 = 0 II. 6y2 + 69y + 198 = 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

Eq I: 2x^2 + 5x + 2 = 0 => (2x+1)(x+2) = 0 => x = -0.5, -2. Eq II: 6y^2 + 69y + 198 = 0 => 2y^2 + 23y + 66 = 0 => (2y+11)(y+6) = 0 => y = -5.5, -6. Comparing values, -0.5 > -5.5 and -0.5 > -6, while -2 > -5.5 and -2 > -6. Thus, x > y.

AI explanation

Use the factorization method on equation I to split the middle term of 2x^2 + 5x + 2 = 0 into 4x and x, yielding (2x + 1)(x + 2) = 0, so the roots of x are -1/2 and -2. For equation II, use the factorization method to split the middle term of 6y^2 + 69y + 198 = 0 into 33y and 36y, yielding (6y + 33)(y + 6) = 0, which gives the roots y = -11/2 and y = -6. Comparing the values, the smallest x is -2 and the largest y is -5.5, which means x > y.

Keep practicing — related questions