complex zeros of f

Question

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

f(x) = x^4 + 26x^2 + 25

 

The complex zeros of f are

Use the complex zeros to factor f.

Answer 1

Let u = x²

 

f(u) = u² + 26u + 25

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

 

f(x) = (x²+25)(x²+1)

f(x) = (x+5i)(x-5i)(x+i)(x-i)     [factored form]

0 = (x+5i)(x-5i)(x+i)(x-i)

 

x = ±5i and ±i                             [zeros]