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

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) (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 and "i", it turns out that comes up pretty often that mathematicians and all of their laziness decided to call "i" the . So this means that . So when we say we really mean . 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.
RELATED QUESTIONS
Find the exact complex number solutions to the quadratic equation using the quadratic... (answered by richwmiller)

ax^2-(2a+1)x+(a+1)=0 Then the product x1x2 is equal to: I know I have to use the... (answered by scott8148)

Four steps to derive the quadratic formula are shown below. I x^2+(-b)/a x=(-c)/a II... (answered by ikleyn)

Problem: Find the inverse of {{{ y = x^2 + sqrt (x) }}}. I've fought the good fight,... (answered by ankor@dixie-net.com)

When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the... (answered by longjonsilver)

How many real numbers does the quadratic equation have 2x^2+7x+9=I Note use formula... (answered by MathLover1)

Please help, We included the table of numbers that we have chosen. Any help, especially... (answered by venugopalramana)

Could you please help me in understanding this problem. I have attempted to use the... (answered by jim_thompson5910)

Developing and Analyzing the Quadratic Formula This formula, which is called the... (answered by stanbon)