Question

Can someone explain me, what is a real root?

Answer 1

A real root is a solution to an equation which is also a real number.

Explanation:

Given an equation in a single variable, a root is a value that can be substituted for the variable in order that the equation holds. In other words it is a "solution" of the equation.

It is called a real root if it is also a real number.

For example:

`x^2-2 = 0`

has two real roots:

`sqrt(2) ~~ 1.414`

`-sqrt(2) ~~ -1.414`

On the other hand:

`x^2+2 = 0`

has no real roots, since `x^2>=0` for any real number `x`.

It does have roots, but they are non-real complex numbers, specifically `sqrt(2)i` and `-sqrt(2)i`.