Multiple choice

Directions: In the following question, two equations (I) and (II) are given. You have to solve both the equations and give answer. (I) 13x2 - 28x + 4 = 0 (II) -4 = 5y2 + 12y

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

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

I: 13x^2 - 28x + 4 = 0. Roots: x = [28 +/- sqrt(784 - 208)] / 26 = [28 +/- sqrt(576)] / 26 = [28 +/- 24] / 26. x = 52/26 = 2 or x = 4/26 = 2/13. II: 5y^2 + 12y + 4 = 0. Roots: y = [-12 +/- sqrt(144 - 80)] / 10 = [-12 +/- 8] / 10. y = -4/10 = -0.4 or y = -20/10 = -2. Since both roots of x are positive and both roots of y are negative, x > y.

AI explanation

For the first equation, 13x2 - 28x + 4 = 0, splitting the middle term gives 13x2 - 26x - 2x + 4 = 0. This factors into (x - 2)(13x - 2) = 0, meaning the roots for x are 2 and 2 divided by 13. For the second equation, 5y2 + 12y + 4 = 0, splitting the middle term gives 5y2 + 10y + 2y + 4 = 0, which factors into (y + 2)(5y + 2) = 0 to yield y roots of -2 and -2 divided by 5. Since both values of x are positive and both values of y are negative, x is greater than y.

Keep practicing — related questions