Multiple choice

In each question two equations numbered I and II are given, you have to solve both the equation and choose the correct answer. (I.) (x^2 - 21x + 108 = 0) (II.) (y^2 -27y + 176 = 0)

  1. $\(x > y\)$
  2. $\(x < y\)$
  3. $\(x \le y\)$
  4. $\(x \ge y\)$

  5. x = y or the relationship can’t be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving equation I: x² - 21x + 108 = 0. Discriminant = 441 - 432 = 9. So x = (21 ± 3)/2, giving x = 12 or x = 9. Solving equation II: y² - 27y + 176 = 0. Discriminant = 729 - 704 = 25. So y = (27 ± 5)/2, giving y = 16 or y = 11. Comparing all cases: 12 < 16 (x < y), 12 > 11 (x > y), 9 < 16 (x < y), 9 < 11 (x < y). Since sometimes x < y and sometimes x > y, the relationship cannot be established.

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