Multiple choice

Directions: In the given question, two equations are given. You have to solve both the equations and mark the correct option. I. 15x2 - 22x + 8 = 0 II. 21y2 - 17y + 2 = 0

  1. x < y

  2. x ≤ y

  3. x > y

  4. x ≥ y

  5. x = y or the relationship cannot be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Equation I: 15x^2 - 22x + 8 = 0. Roots: x = (22 +/- sqrt(484 - 480))/30 = (22 +/- 2)/30. x = 24/30 = 0.8 or 20/30 = 0.66. Equation II: 21y^2 - 17y + 2 = 0. Roots: y = (17 +/- sqrt(289 - 168))/42 = (17 +/- 11)/42. y = 28/42 = 0.66 or 6/42 = 0.14. Comparing roots: 0.8 >= 0.66 and 0.8 >= 0.14 and 0.66 >= 0.66 and 0.66 >= 0.14. Thus x >= y.

AI explanation

First, factor equation I, 15x2 - 22x + 8 = 0, to get (5x - 2)(3x - 4) = 0, which gives the roots x = 2/5 and x = 4/3. Next, factor equation II, 21y2 - 17y + 2 = 0, to get (7y - 2)(3y - 1) = 0, giving the roots y = 2/7 and y = 1/3. When we compare the values, 2/5 is greater than 2/7, and 4/3 is greater than 1/3, meaning every possible value of x is greater than every possible value of y. Therefore, the relationship is x >= y.

Keep practicing — related questions