To find the equation that has the solutions for x² + 2x + 4 = 0, we first need to consider what it means to solve a quadratic equation. The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants.
In this case, we have:
- a = 1
- b = 2
- c = 4
Next, we can apply the quadratic formula to determine the solutions:
x = (-b ± √(b² – 4ac)) / 2a
For our equation:
- Calculate b² – 4ac:
(2)² – 4(1)(4) = 4 – 16 = -12
Since the discriminant (-12) is negative, this tells us that the solutions will be complex (imaginary) numbers. We can simplify this further:
x = (-2 ± √(-12)) / 2(1)
This can be rewritten as:
x = (-2 ± 2i√3) / 2
So the solutions can be expressed as:
x = -1 ± i√3
In conclusion, the equation that has the solutions x² + 2x + 4 = 0 is indeed the correct quadratic equation for the given solutions, which results in complex numbers.