Multiple choice

The product of two consecutive positive integers is 306, the smaller integer being x. Which of the following quadratic equations represents this situation?

  1. x2 + x – 306 = 0

  2. x2 + x + 306 = 0

  3. 2x2 + x – 306 = 0

  4. x2 – 305 = 0
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A Correct answer
Explanation

Let the smaller integer be x. The next consecutive integer is x + 1. Their product is x(x + 1) = 306, which simplifies to x^2 + x = 306, or x^2 + x - 306 = 0.

AI explanation

Let the two consecutive positive integers be x and x + 1. Their product is expressed as x times (x + 1) = 306. Expanding the left side yields the quadratic equation x^2 + x - 306 = 0.

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