To solve the quadratic equation x² + 2x + 4 = 0 using the quadratic formula, we first need to identify the coefficients a, b, and c in the standard form of a quadratic equation ax² + bx + c = 0.
Here, we have:
- a = 1
- b = 2
- c = 4
The quadratic formula is given by:
x = (-b ± √(b² – 4ac)) / (2a)
Next, we need to calculate the discriminant, which is inside the square root:
b² – 4ac = (2)² – 4(1)(4) = 4 – 16 = -12
Since the discriminant is negative (-12), this means there are no real solutions. However, we can still find complex solutions using the quadratic formula.
Now we can substitute the values of a, b, and the discriminant into the formula:
x = (-2 ± √(-12)) / (2 * 1)
Calculating further, we take the square root of -12. We can write this as:
√(-12) = √(12) * √(-1) = 2√3 * i
Now substituting this back into the formula gives us:
x = (-2 ± 2√3i) / 2
We can simplify this expression:
x = -1 ± √3i
Thus, the solutions to the equation x² + 2x + 4 = 0 are:
- x = -1 + √3i
- x = -1 – √3i