[Coda]

Yeah, you can more or less ignore them when you're graphing.

As for WHAT an imaginary root is...

The real numbers aren't the only kinds of numbers you can work with using standard algebra. There's an extension of the real numbers called complex numbers: a complex number is the sum of a real number an an imaginary number.

Complex numbers allow you to have meaningful values for some things that the real numbers fail at. The most significant use is also the fundamental definition: The imaginary number i is equal to the square root of -1. And just as all real numbers are multiples of the basis 1, all imaginary numbers are multiples of the basis i, and so all complex numbers can be expressed in the form a + bi.

The square of any complex number is a real number. Unlike real numbers, though, where x² is always positive, the square of a complex number may well be negative.

The norm of a complex number (a + bi) is sqrt(a² + b²). This is an extension of the notion of absolute value: you'll notice it's equal to the absolute value for numbers without an imaginary part.

So what is an imaginary root?

Well, complex numbers work just fine and dandy in polynomials. You can multiply and add complex numbers just fine as long as you remember the identity i * i = -1. So if a real root is a solution to p(x) = 0 where x = a + 0i, then an imaginary root is a solution to p(x) = 0 where x = 0 + bi.