# Write a quadratic equation with imaginary numbers table

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. These roots are identical except for the "sign" separating the two terms.

These are all equal representations of both of the roots. So 2 times 2 is 4. Or 3 minus i over 2. The variables a, b, and c in the quadratic formula correspond to the coefficients in the quadratic equation.

This negative square root creates an imaginary number. And we want to verify that that's the same thing as 6 times this quantity, as 6 times 3 plus i over 2.

### Quadratic formula

And standard form, of course, is the form ax squared plus bx plus c is equal to 0. All of that over 2 times a. Substituting these values into the quadratic formula provides the expression below: Start by simplifying your denominator. We have a 4 plus 5. We have 8 minus 6i. So this is 2 times-- let me just square this. Or 3 minus i over 2.

So 3 times 3 is 9. All of that over 2 times a. So this is 2 times-- let me just square this.

So that's also negative 1. And then you're going to have two of those.

## Write a quadratic equation with imaginary numbers table

Once again, a little hairy. So this solution, 3 plus i, definitely works. So once again, just looking at the original equation, 2x squared plus 5 is equal to 6x. However, some may not realize you can also perform the reverse operation to derive the equation from the points. It's going to get a little bit hairy, because we're going to have to square it and all the rest. Or you could go directly from this. So plus 6i. Source: This work is adapted from Sophia author Colleen Atakpu. When you add them, you get 6i. And then you're going to have two of those. Now what I want to do is a verify that these work. We have a 4 plus 5. In the complex number below, 5 is the real part of the complex number, and 3i is the imaginary part. Furthermore, in the imaginary part, 3 is the coefficient and i is the imaginary unit.

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