Final answer:
The equation with the solutions x = 1 ± √(5) is obtained by forming and expanding the factors (x - (1 + √(5)))(x - (1 - √(5))) which simplifies to x^2 - 2x - 4 = 0.
Step-by-step explanation:
To determine which equation has the solutions x = 1 ± √(5), we need to start with the solutions and work backwards to form the equation. Starting with the solutions given, we can express the solutions in the form (x - a)(x - b) = 0, where a and b are the solutions to the equation. In this case, a is 1 + √(5) and b is 1 - √(5).
The factors of the equation are thus (x - (1 + √(5)))(x - (1 - √(5))) = 0. If we expand this expression, we get:
x^2 - x(1 + √(5)) - x(1 - √(5)) + (1 + √(5))(1 - √(5)) = 0
Simplifying further, we get:
x^2 - x - x + 1 - 5 = x^2 - 2x - 4 = 0
Hence, the correct equation is d. x^2 - 2x - 4 = 0.