Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 329: 32

$x\in \{-\sqrt 5i, \sqrt 5i\}$, each with a multiplicity of $2$

$Q(x)=x^4+10x^2+25$ The polynomial is the perfect square: $Q(x)=x^4+10x^2+25=(x^2+5)^2=(x^2+5)(x^2+5)=(x-\sqrt 5i)(x+\sqrt 5i)(x-\sqrt 5i)(x+\sqrt 5i)$, thus $x^4+10x^2+25=(x-\sqrt 5i)^2(x+\sqrt 5i)^2$ Its zeros are: $x\in \{-\sqrt 5i, \sqrt 5i\}$, each with a multiplicity of $2$