Multiple choice

Following question contains two equations as I and II. You have to solve both equations and determine the relationship between them. I) x2– 32x + 247 = 0 II) y2– 35y + 304 = 0

  1. x > y

  2. x ≥ y

  3. x = y or relationship can't be determined.

  4. x < y

  5. x ≤ y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For I: x^2 - 32x + 247 = 0, the roots are 13 and 19. For II: y^2 - 35y + 304 = 0, the roots are 16 and 19. Comparing the sets {13, 19} and {16, 19}, we see that x can be less than, equal to, or greater than y depending on the specific root chosen, so the relationship cannot be determined.

AI explanation

Using the factorization method for the first equation, x squared minus 32x plus 247 equals zero gives the factors (x minus 13) and (x minus 19), so x equals 13 or 19. For the second equation, y squared minus 35y plus 304 equals zero factors into (y minus 16) and (y minus 19), so y equals 16 or 19. Since x equals 19 is greater than y equals 16, but x equals 13 is less than y equals 16 and y equals 19, the relationship cannot be definitively established between the variables.

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