Write a polynomial equation with integral coefficients whase zeros are 3 and \( 2 i \).

To construct a polynomial equation with integral coefficients and given zeros of 3 and \(2i\), we must also include the conjugate of \(2i\), which is \(-2i\). The polynomial can be determined from these zeros as follows: 1. The factors corresponding to the zeros are \((x - 3)\), \((x - 2i)\), and \((x + 2i)\). 2. The polynomial can be formed by multiplying these factors: \[ P(x) = (x - 3)\left((x - 2i)(x + 2i)\right). \] 3. Simplifying \((x - 2i)(x + 2i)\) gives: \[ (x - 2i)(x + 2i) = x^2 + 4. \] 4. Substituting back, we have: \[ P(x) = (x - 3)(x^2 + 4). \] 5. Expanding this gives us our polynomial: \[ P(x) = x^3 - 3x^2 + 4x - 12. \] So the polynomial equation with integral coefficients is: \[ x^3 - 3x^2 + 4x - 12 = 0. \]