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

1 Answer
Jan 10, 2017

Answer:

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.