Determine the coefficients of the quadratic equation with roots 1/2 and -1.

The quadratic equation with roots 1/2 and -1 has coefficients of 2x^2 - 3/2x - 1.

To determine the coefficients of the quadratic equation with roots 1/2 and -1, we can use the fact that if a quadratic equation has roots r and s, then the equation can be written as (x - r)(x - s) = 0.

So, for the given roots of 1/2 and -1, the quadratic equation can be written as (x - 1/2)(x + 1) = 0.

Expanding this equation gives us:

x^2 + (1/2)x - x/2 - 1/2 = 0

Simplifying this equation gives us:

x^2 - 1/2x - 1/2 = 0

Therefore, the coefficients of the quadratic equation with roots 1/2 and -1 are 1, -1/2, and -1/2, which can be written as 2x^2 - 3/2x - 1.