Multiple choice

In each of the following questions two equations are given. Solve these equations and give answer: (I) (2x^2 - 4.2x + 1.8 = 0) (II) (y^2 - 4.8y + 5.4 = 0)

  1. If x < y

  2. If x > y

  3. If x ≥ y

  4. If x ≤ y

  5. If x = y or no relationship can be established between x and y.
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A Correct answer
Explanation

Solving equation I: 2x² - 4.2x + 1.8 = 0. Using quadratic formula: x = [4.2 ± √(17.64-14.4)]/4 = [4.2 ± √3.24]/4 = [4.2 ± 1.8]/4, giving x = 1.5 or x = 0.6. Solving equation II: y² - 4.8y + 5.4 = 0 gives y = [4.8 ± √(23.04-21.6)]/2 = [4.8 ± √1.44]/2 = [4.8 ± 1.2]/2, giving y = 3 or y = 1.8. Since all values of x (0.6, 1.5) are less than all values of y (1.8, 3), x < y.

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