The quadratic equation 2x² + 4x + 12 = 0 has no real solutions.
To understand why, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
Here, a = 2, b = 4, and c = 12. We first need to calculate the discriminant, which is b² – 4ac.
Calculating the discriminant:
b² = 4² = 16
4ac = 4 * 2 * 12 = 96
Now, substituting these values into the discriminant:
Discriminant = 16 – 96 = -80
Since the discriminant is negative (-80), it indicates that there are no real solutions to this equation. Instead, there will be two complex solutions. This means the quadratic graph does not intersect the x-axis.