Multiple choice

Directions: In the following question, two equations are given. You have to solve both the equations and then choose the correct option. 5x2 − 310x + 3000 = 0 7y2 + 80y - 1500 = 0

  1. x > y

  2. x < y

  3. x ≥ y

  4. x ≤ y

  5. x = y or there is no relation between x and y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

5x^2 - 310x + 3000 = 0 => x^2 - 62x + 600 = 0. (x-50)(x-12)=0. x=50, 12. 7y^2 + 80y - 1500 = 0. y = [-80 +/- sqrt(6400 - 4*7*-1500)] / 14 = [-80 +/- sqrt(6400 + 42000)] / 14 = [-80 +/- 220] / 14. y = 140/14 = 10 or -300/14 = -21.4. Comparing roots: 50 > 10, 50 > -21.4, 12 > 10, 12 > -21.4. Thus x > y.

AI explanation

Using the method of splitting the middle term, the first equation 5x^2 - 310x + 3000 = 0 yields roots x = 60 and x = 10. The second equation 7y^2 + 80y - 1500 = 0 yields roots y = 10 and y = -150/7. Comparing the values, both roots of x are either greater than or equal to the roots of y. Therefore, the established relationship is x > y.

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