Final answer:
The simplest polynomial with zeros of 2i, sqrt(3), and 1 can be constructed by multiplying the factors associated with these zeros including the conjugate pair of the complex zero. The polynomial is f(x) = (x^2 + 4)(x - √3)(x - 1).
Step-by-step explanation:
The simplest polynomial with zeros of 2i, sqrt(3), and 1 can be found using the fact that if a polynomial has a complex zero, its conjugate is also a zero. The zeros 2i and -2i (the conjugate of 2i) will give us the quadratic (x - 2i)(x + 2i), which simplifies to x² + 4. The zero sqrt(3) gives us a linear factor (x - sqrt(3)), and the zero 1 gives us (x - 1). Multiplying these factors together, we get the polynomial:
f(x) = (x^2 + 4)(x - √3)(x - 1).
By expanding and simplifying the terms, we arrive at the simplest polynomial that has the given zeros.