# Write a quadratic equation with imaginary numbers in real life

Indeed, if you make any error at all in estimating the initial insect populations then very soon your prediction will be hopelessly wrong. Now point out that you have used fractions, non-integer numbers, in a problem where they have no physical relevance.

And now we're going to try this root, verify that it works. So we verified that both of these complex roots, satisfy this quadratic equation.

Negative 4, if I take a square root, I'm going to get an imaginary number. This 2 and this 2 are going to cancel out. I'm not scared of you any more! When you add them, you get 6i. You can point out that this happens all the time in engineering applications.

## Write a quadratic equation with imaginary numbers in real life

You can't measure populations in fractions; you can't have "half a person", for example. In the same way, being willing to think about what happens in the larger set of complex numbers allows us to draw conclusions about real world situations even when actual measurements in that particular real world situation only involve the real numbers. The roots belong to the set of complex numbers, and will be called "complex roots" or "imaginary roots". Now we have the position of x2 on the x-axis and can repeat the process. So draw a vertical line from x1 until it hits the graph. And so our left hand side becomes 2x squared minus 6x plus 5 is equal to-- and then on our right hand side, these two characters cancel out, and we just are left with 0. Then we have a plus 5 needs to be equal to 9 minus 3i. So let's do that in this scenario.

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