Multiple choice

Directions: In this question, two equations are given. You have to solve both the equations and mark the correct option. (i) 6x2 - 43x + 77 = 0 (ii) 10y2 - 327y + 2501 = 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

6x^2 - 43x + 77 = 0. Roots are (43 +/- sqrt(1849 - 1848))/12 = (43 +/- 1)/12. x = 44/12 = 3.66 or x = 42/12 = 3.5. 10y^2 - 327y + 2501 = 0. Roots are (327 +/- sqrt(106929 - 100040))/20 = (327 +/- sqrt(6889))/20 = (327 +/- 83)/20. y = 410/20 = 20.5 or y = 244/20 = 12.2. Clearly x < y.

AI explanation

For the first equation 6x2 - 43x + 77 = 0, we find two numbers that multiply to 462 (6 multiplied by 77) and add to -43, which allows us to factor it into (2x - 7)(3x - 11) = 0, giving x = 3.5 or x = 3.66. For the second equation 10y2 - 327y + 2501 = 0, the factors are (10y - 61)(y - 41) = 0, meaning y = 6.1 or y = 41. Since both values of x are smaller than both values of y, x is always less than y.

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