Multiple choice

Directions: Equations I and II are given. You have to solve both the equations and choose the correct answer. I. 50x2 = 51x - 1 II. 2y2 + 31y + 29 = 0

  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
A Correct answer
Explanation

I: 50x^2 - 51x + 1 = 0. Roots are (51 +/- sqrt(51^2 - 200))/100 = (51 +/- 49)/100. x = 1 or 0.02. II: 2y^2 + 31y + 29 = 0. Roots are (-31 +/- sqrt(31^2 - 232))/4 = (-31 +/- 27)/4. y = -1 or -14.5. Comparing roots, x > y.

AI explanation

Rearrange the first equation into standard form to get 50x2 - 51x + 1 = 0, then factor it by splitting the middle term to find the roots x = 1 and x = 1/50. Factor the second equation as (2y + 1)(y + 29) = 0 to get the roots y = -0.5 and y = -29. Since all values of x are positive and all values of y are negative, x is strictly greater than y.

Keep practicing — related questions