Eli5: What are real and non real roots?

Question

I keep googling it and I still don’t understand what they are and their differences 😭😭

In: 18

Answer 1

A root of an equation is a number where that equation is equal to zero. Some expressions, like x^2 – 4, have real roots. In this case the expression is zero when x = 2 or x = -2.

Other expressions, like x^2 + 4 have no real numbers that can make them equal zero. There are, however, complex numbers that can. Recall a complex number is a number that includes the imaginary unit i, where i = sqrt(-1). We can set x = 2i, and that means x^2 = -4. So the expression x^2 + 4 becomes -4 + 4 = 0 and we say that the expression has a complex root at x = 2i.