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

The quadratic equation with roots 1/2 and -1/2 has coefficients 4, 0, and -1.

To find the quadratic equation with roots 1/2 and -1/2, we start with the fact that the equation can be written in the form:

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

Expanding this expression gives:

x^2 - (1/2)x + (1/2)x - 1/4 = 0

Simplifying, we get:

x^2 - 1/4 = 0

To put this equation in standard form, we need to multiply both sides by 4:

4x^2 - 1 = 0

So the coefficients of the quadratic equation are 4, 0, and -1. The coefficient of x^2 is 4, the coefficient of x is 0 (since there is no x term), and the constant term is -1. Therefore, the quadratic equation with roots 1/2 and -1/2 is:

4x^2 - 1 = 0