Multiple choice

Directions: In this question, two equations are given. You have to solve both the equations and mark the correct option. (i) 77x2 - 1078x + 3465 = 0 (ii) y2 - 39y + 338 = 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

Eq (i): 77x^2 - 1078x + 3465 = 0. Divide by 77: x^2 - 14x + 45 = 0. (x-9)(x-5)=0, so x=9 or 5. Eq (ii): y^2 - 39y + 338 = 0. (y-13)(y-26)=0, so y=13 or 26. Comparing roots: 9 < 13, 9 < 26, 5 < 13, 5 < 26. Thus x < y.

AI explanation

For the first equation 77x2 - 1078x + 3465 = 0, we find the prime factorizations and factor it by grouping to get (7x - 45)(11x - 77) = 0, which simplifies to x = 6.42 or x = 7. For the second equation y2 - 39y + 338 = 0, the numbers 13 and 26 multiply to 338 and add to 39, so y = 13 or y = 26. When comparing the values, both possible values of x are strictly less than both possible values of y. Therefore, x is always less than y.

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