# Write a quadratic equation with imaginary numbers definition

So this right over here is going to be 2i. This and this or this and this, or this. This is 3 plus or minus i over 2. All I did-- you can see that this is just dividing both of these by 2.

### Find quadratic equation given complex roots calculator

So it also checks out. Once again, a little hairy. That's if I take the positive version of the i there. The imaginary unit number is i. If x can be any complex number, then y x may be complex itself. These roots are identical except for the "sign" separating the two terms. So plus 6i. Let's now take a closer look at how these numbers relate to quadratics. Wait a moment - did you notice something wrong there?

Let's now take a closer look at how these numbers relate to quadratics. And if that doesn't make sense to you, I encourage you to kind of multiply it out either with the distributive property or FOIL it out, and you'll get the middle term. Times 2 over here, plus 5, needs to be equal to-- well, before I even multiply it out, we could divide the numerator and the denominator by 2.

So 6 divided by 2 is 3. And the quadratic formula tells us that if we have something in standard form like this, that the roots of it are going to be negative b plus or minus-- so that gives us two roots right over there-- plus or minus square root of b squared minus 4ac over 2a.

So let's do that. Or you could go directly from this. So what we want to do is we want to take 2 times this quantity squared. The discriminant, b2 - 4ac, offers valuable information about the "nature" of the roots of a quadratic equation where a, b and c are rational values. 