To solve the quadratic equation 2x² + 3x + 1 = 0, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a = 2, b = 3, and c = 1. First, we calculate the discriminant:
D = b² – 4ac
D = 3² – 4(2)(1) = 9 – 8 = 1
Since the discriminant is positive (D > 0), we know there are two distinct real solutions. Now we can apply the quadratic formula:
x = (−3 ± √1) / (2 × 2)
This gives us:
x₁ = (−3 + 1) / 4 = -2 / 4 = -0.5
x₂ = (−3 − 1) / 4 = −4 / 4 = -1
Therefore, the solutions to the equation 2x² + 3x + 1 = 0 are:
- x₁ = -0.5
- x₂ = -1