Multiple choice

Directions: In the given question, two equations are given. You have to solve both the equations and mark the correct option. (1) x2 - 5.2x + 6.51 = 0 (2) y2 - 9.2y + 20.91 = 0

  1. x > y

  2. x < y

  3. x ≤ y

  4. x ≥ y

  5. The relationship between x and y cannot be established.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

(1) x^2 - 5.2x + 6.51 = 0. Roots: x = [5.2 +/- sqrt(27.04 - 26.04)] / 2 = [5.2 +/- 1] / 2. Roots: 3.1, 2.1. (2) y^2 - 9.2y + 20.91 = 0. Roots: y = [9.2 +/- sqrt(84.64 - 83.64)] / 2 = [9.2 +/- 1] / 2. Roots: 5.1, 4.1. Comparing all pairs: 3.1 < 5.1, 3.1 < 4.1, 2.1 < 5.1, 2.1 < 4.1. Thus x < y.

AI explanation

To clear decimals, multiply the first equation by 100 to get 100x2 - 520x + 651 = 0, which factors into (10x - 30)(10x - 21.7) = 0 for roots x = 3 and x = 2.17. Similarly, the second equation becomes 100y2 - 920y + 2091 = 0, which factors into (10y - 30)(10y - 69.7) = 0 for roots y = 3 and y = 6.97. Comparing the values, the largest root of x is 3, which is less than the largest root of y at 6.97. Therefore, x is strictly less than y.

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