Multiple choice

x2 - 6x - 567 = 0. It is given that x is a real number. Column A Column B x 27 Compare the two quantities to decide whether

  1. the quantity in Column A is greater

  2. the quantity in Column B is greater

  3. the two quantities are equal

  4. the relationship cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The quadratic equation x^2 - 6x - 567 = 0 can be solved using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a. This yields x = (6 +/- sqrt(36 + 2268)) / 2 = (6 +/- sqrt(2304)) / 2 = (6 +/- 48) / 2, resulting in x = 27 or x = -21. Since x can be either 27 or -21, the relationship between x and 27 cannot be determined.

AI explanation

Using the quadratic formula, x = (6 ± sqrt((-6)^2 - 4(1)(-567))) / 2(1), which simplifies to x = (6 ± sqrt(36 + 2268)) / 2. This yields x = (6 ± sqrt(2304)) / 2, giving x = (6 ± 48) / 2. Therefore, x can be 27 or -21, meaning its exact value is ambiguous and cannot be definitively compared to 27.

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