Final answer:
The correct equation with solutions x = 1 ± √5 is x^2 - 2x - 4 = 0. By matching the given solutions to the form of the quadratic formula, it's determined that option 4 fits the required coefficients to produce the desired roots.
Step-by-step explanation:
The student is asking which equation has the solutions x = 1 ± √5. To identify the correct equation, we need to consider the fact that the solutions provided are in the form that would result from using the quadratic formula, which is typically x = √{-b ± √{b^2-4ac}}/2a for a quadratic equation ax^2+bx+c = 0.
Since the solutions are x = 1 ± √5, this implies that:
- The coefficient of x (the b value) must be the opposite of twice the constant term (the x-intercept), so b = -2(1) = -2.
- The constant term (the c value) when substituted into the quadratic formula equation √{b^2-4ac} should give ±√5 after simplification.
The only equation that fits this description is x^2 - 2x - 4 = 0. Checking:
- b^2-4ac becomes (-2)^2 - 4(1)(-4) which simplifies to 4 + 16, resulting in √20.
- Since √20 is the same as 2√5 and the quadratic formula divides this value by 2a (with a being 1 in this case), it reduces back to ±√5.
Therefore, the correct equation is x^2 - 2x - 4 = 0, which is option 4.