Polynomials: Why Irrational and Imaginary Roots come in Pairs

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This video shows why, when finding roots of polynomials, that irrational roots and imaginary roots come in pairs.
  1. Kelly Bow
  2. Polynomials;theorems
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@kevin4849 In the context of Quadratic functions, irrational and imaginary roots do come in pairs, both the + and - roots. The same would go with 4th roots, there were be two sets of pairs. This doesn't apply to x^2 = depending on context, roots may be extraneous.

MrsBowsMathClass
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Irrational roots don't always come in pairs. For example, the polynomial x^3-2=0 has only one root which is the cube root of 2. Here's my question: do even-numbered irrational roots come in pairs? In other words, roots of the form A+B*(nth root of) C always come in pairs, when n is positive and even?

kevinc