Multiple choice

Directions: Equation I and II are given. You have to solve both the equations and find out the relation, if any between x and y. I. 3x2 + 18x + 15 = 0 II. 14y2 + 3y = 2

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or no relationship can be established between 'x' and 'y'.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

I: 3x^2 + 18x + 15 = 0 -> x^2 + 6x + 5 = 0 -> (x+5)(x+1)=0, so x = -5, -1. II: 14y^2 + 3y - 2 = 0 -> 14y^2 + 7y - 4y - 2 = 0 -> 7y(2y+1) - 2(2y+1) = 0 -> (7y-2)(2y+1)=0, so y = 2/7, -1/2. Comparing values, x < y.

AI explanation

Dividing equation I by 3 yields x2 + 6x + 5 = 0, which factors to (x + 5)(x + 1) = 0, giving x = -5 and x = -1. Rewriting equation II gives 14y2 + 3y - 2 = 0, which factors to (7y - 2)(2y + 1) = 0, resulting in y = 2/7 and y = -1/2. Since both negative values of x are strictly less than both values of y, x < y.

Keep practicing — related questions