Question

How do you find the complex roots of `x+8=0`?

Answer 1

This equation has one real (complex) root, namely `x = -8`

Explanation:

Given:

`x+8=0`

This is a polynomial equation of degree `1`, also known as a linear equation.

We can subtract `8` from both sides of the equation to find:

`x = -8`

This is the only root.

`-8` is a Real number, but it is also a Complex number since the Real numbers are a subset of the Complex numbers.

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Footnote

The Fundamental Theorem of Algebra (FTOA) tells us that any non-constant polynomial has a zero in the Complex numbers.

A straightforward corollary of the FTOA, often stated with it, is that a polynomial of degree `n > 0` has exactly `n` Complex (possibly Real) zeros.

So a linear equation has exactly one root, a quadratic equation has two, a cubic has three, etc.