Question

Write the simplest polynomial function with the given roots: 2i, sqrt(3), 4.

Answer 1

(x - 2i)(x + 2i)(x - √3)(x - 4) = (x^2 + 4)(x^2 - 4x - √3x + 4√3) = x^4 - 4x^3 - √3x^3 + 4√3x^2 + 4x^2 - 16x - 4√3x + 16√3 = x^4 - (4 + √3)x^3 + 4(√3 + 1)x^2 - 4(4 - √3)x + 16√3