# Find the complex zeros of the following polynomial function. Write f in factored form. f(x) = x^{4} + 26x^{2} + 25

**Solution:**

Using the u- substitution in the given polynomial we have,

Let u = x^{2}

f(u) = u^{2} + 26u + 25 is a quadratic equation. By splitting middle terms we get

f(u) = u^{2} + 25u + u + 25

= u(u + 25) + 1(u + 25)

= (u + 1)(u + 25)

To find the zeros of the above equation we put,

f(u) = (u +1)(u + 25) = 0

u = -1 and u = -25

Since u = x^{2} we get the solution for x as

x^{2} = -1 ⇒ x = ± i

Also u = -25 which implies

x^{2} = -25 ⇒ x = ± 5 i

## Find the complex zeros of the following polynomial function. Write f in factored form.

**Summary:**

The complex zeros of the following polynomial function f(x) = x^{4} + 26x^{2} + 25 are x = ± i and x = ± 5 i.

Math worksheets and

visual curriculum

visual curriculum