SOLUTION: How did they come up with the quadratic formula x=-b+ b^s-4AC/2A? and what is the purpose of imaginary numbers such as -1 and i? I don't have a square root symbol so the negative

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How did they come up with the quadratic formula x=-b+ b^s-4AC/2A? and what is the purpose of imaginary numbers such as -1 and i? I don't have a square root symbol so the negative       Log On


   

Question 204120: How did they come up with the quadratic formula x=-b+ b^s-4AC/2A? and what is the purpose of imaginary numbers such as -1 and i? I don't have a square root symbol so the negative 1 is to have a sqrt. sympbol and also for the problem for the quadratic formula. Thank you you knowledge is very appreciated!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Well there's a long derivation to find the quadratic formula (which I'm sure that it will take a while to type up), but you can find a derivation here.

As for sqrt%28-1%29 and "i", it turns out that sqrt%28-1%29 comes up pretty often that mathematicians and all of their laziness decided to call "i" the sqrt%28-1%29. So this means that i=sqrt%28-1%29. So when we say 2%2B3i we really mean 2%2B3%2Asqrt%28-1%29. This notation saves a lot of time writing and helps with calculations.


As for why imaginary numbers are useful, you probably need to be a little more patient. There are a number of applications in physics (such as electrical engineering) that imaginary and complex numbers are useful in. I honestly cannot tell you which ones specifically as I'm not an engineer. I'm pretty sure that there are other uses, I just can't think of them right now.