Question

For each polynomial function, one zero is given. Find all other zeros. f(x) = x⁴ + 26x² + 25; i

Answer 1

To find the other zeros of the polynomial function f(x) = x⁴ + 26x² + 25, use the fact that complex zeros come in conjugate pairs. The other zeros are -i and i.

Step-by-step explanation:

To find the other zeros of the polynomial function f(x) = x⁴ + 26x² + 25, we can use the fact that complex zeros come in conjugate pairs. Since i is given as a zero, its conjugate -i must also be a zero.

We can set up the equation (x - i)(x + i) = 0 and solve for x to find the other zeros. Expanding the equation, we get x² - i² = 0, which simplifies to x² + 1 = 0.

Therefore, the other zeros of the polynomial function are x = i and x = -i. So, the complete set of zeros for f(x) = x⁴ + 26x² + 25 is {-i, i}.