Question

1. jake is three years older than doug, and the product of their ages is 40. write a quadratic equation that represents the situation where x represents dougs age.

\\( x^2 - 3x - 40 = 0 \\)
\\( x^2 + 3x + 40 = 0 \\)
\\( x^2 - 3x + 40 = 0 \\)
\\( x^2 + 3x - 40 = 0 \\)

Explanation:

Step1: Define Variables

Let \(x\) be Doug's age. Then Jake's age is \(x + 3\) (since Jake is 3 years older than Doug).

Step2: Set Up the Equation

The product of their ages is 40, so we have the equation \(x(x + 3)=40\).

Step3: Expand and Rearrange

Expanding the left - hand side gives \(x^{2}+3x = 40\). Then, subtracting 40 from both sides to get the quadratic equation in standard form: \(x^{2}+3x - 40 = 0\).

Answer:

\(x^{2}+3x - 40 = 0\)