Question

The average of a positive number, its square and 3 is 5. Find the number.

• A. 2
• B. 3
• C. 1
• D. 5

Answer 1

The Correct Option is B

To find the number, let the positive number be \( x \). According to the problem, the average of the number (\( x \)), its square (\( x^2 \)), and 3 is 5. We can set up the equation for the average as follows:

\[\frac{x + x^2 + 3}{3} = 5\]

To eliminate the fraction, multiply both sides by 3:

\[x + x^2 + 3 = 15\]

Subtract 3 from both sides to simplify the equation:

\[x + x^2 = 12\]

Reorganizing gives us a standard quadratic equation:

\[x^2 + x - 12 = 0\]

To solve this quadratic equation, we need to factor it. We are looking for two numbers that multiply to -12 and add up to 1 (the coefficient of \( x \)). These numbers are 4 and -3. Therefore, we can factor the quadratic as:

\[(x + 4)(x - 3) = 0\]

Setting each factor equal to zero gives potential solutions:

\[x + 4 = 0 \quad \text{or} \quad x - 3 = 0\]

Solving these equations, we find:

\[x = -4 \quad \text{or} \quad x = 3\]

Since the problem specifies that the number is positive, the solution must be \( x = 3 \).

Therefore, the number is 3.