Question

If the product of two consecutive integers is 306, then the quadratic representation of this condition is

• A. x²+x-306=0
• B. x²+x+306=0
• C. x²-x+306=0
• D. x²-x-306=0

Answer 1

The Correct Option is A, D

Step 1: Define the integers.

Let the smaller integer be \( x \). Then the next consecutive integer is \( x + 1 \).

Step 2: Write the product condition.

The product of the two integers is:

\[ x(x + 1) = 306. \]

Expand:

\[ x^2 + x = 306. \]

Rearrange into standard quadratic form:

\[ x^2 + x - 306 = 0. \]

Final Answer: The quadratic representation is \( \mathbf{x^2 + x - 306 = 0} \), which corresponds to option \( \mathbf{(1)} \).