Multiple choice

Directions: In the given question, equations numbered I and II are given. Solve both equations and give answer. I. 225y2 - 105y - 44 = 0 II. 210x2 - 319x + 121 = 0

  1. x > y

  2. x ≤ y

  3. x ≥ y

  4. x < y

  5. x = y or relation between x and y cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Solving 225y^2 - 105y - 44 = 0 gives y = 0.733 or -0.266. Solving 210x^2 - 319x + 121 = 0 gives x = 1.1 or 0.523. Comparing the roots, x >= y is the correct relationship.

AI explanation

Factoring the first equation yields (15y + 4)(15y - 11) = 0, giving roots of y = -4/15 and y = 11/15. Factoring the second equation yields (10x - 11)(21x - 11) = 0, so the roots are x = 11/10 and x = 11/21. Since both roots of x are positive and both roots of y are either negative or a smaller positive fraction, x is always greater than or equal to y.

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