Find the roots of the quadratic equation 2x^2 + 3x + 1 = 0.

The roots of the quadratic equation 2x^2 + 3x + 1 = 0 are -1 and -0.5.

To find the roots of a quadratic equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this equation, a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

Using this formula for the given equation, we get:

x = (-3 ± √(3^2 - 4(2)(1))) / 2(2)
x = (-3 ± √1) / 4

Simplifying this expression, we get:

x = (-3 + 1) / 4 or x = (-3 - 1) / 4
x = -0.5 or x = -1

Therefore, the roots of the quadratic equation 2x^2 + 3x + 1 = 0 are -1 and -0.5. We can check this by substituting these values into the original equation and verifying that they make the equation true.