Final answer:
To find a polynomial function with given zeros, follow these steps: 1. If the zeros are real numbers, write the function as the product of linear factors. 2. If the zeros are imaginary numbers, use complex conjugates. 3. If the zeros are complex or rational numbers, follow the same approach as for imaginary or real numbers respectively.
Step-by-step explanation:
To find a polynomial function with given zeros, we need to use the fact that the zeros of a polynomial are the values of x that make the polynomial equal to zero.
If the zeros are real numbers, we can simply write the function as the product of linear factors. For example, if the zeros are 2 and 5, the function would be (x - 2)(x - 5).
If the zeros are imaginary numbers, we can use the fact that complex conjugates always come in pairs. For example, if the zeros are 2i and -2i, the function would be (x - 2i)(x + 2i).
If the zeros are complex numbers, we can use the same approach as for imaginary numbers. For example, if the zeros are 2 + 3i and 2 - 3i, the function would be (x - (2 + 3i))(x - (2 - 3i)).
Finally, if the zeros are rational numbers, we can use the same approach as for real numbers. For example, if the zeros are 1/2 and 3/4, the function would be (2x - 1)(4x - 3).