Write the polynomial function in standard form with the given roots. x = −i and x = √6

Question

So confusing to me.................

Answer 1

If a root is complex, then its complex conjugate must be a root. If a square root is a root, so is its square root conjugate.

Thus, we have -i, i, √6, -√6 as roots.

Then, our polynomial is (x + i)(x - i)(x - √6)(x + √6) = (x² + 1)(x² - 6) or x⁴ -5x² - 6

Answer 2

If I understand correctly what you ask then the answer is:

The polynomial x^2-6 has real coefficients and roots sqrt(6), -sqrt(6).

The polynomial x^2+1 has real coefficients and roots i, and -i.

Therefore, the polynomial (x^2+1)(x^2-6) has real coefficients and roots the numbers -i, sqrt(6).