Quadratic Formula
The quadratic formula is a quick(unless you can factorise) way of solving quadratic equations. You basically take the coefficient’s of x, x2 and numbers, put then in the formula, work out the two answers and have your 2 solutions of x. And if that wasn’t easy enough written a console program in c++ that will solve them for you(and gives dodgy answers for complex solution ie) imaginary answers when there are no real roots.
so for the general quadratic
ax2+bx+c=0
So what do you do, well enter a, b and c from the general equation into the formula, work out the answers and they are your solutions.
Whats the plus/minus thingy. You might be wondering what the thing is after the -b, well its a plus or minus sign. Because when you work out a square root it can have to answers, eg)root 9 = +3 and -3, he formula takes this into account by saying you must use the plus and the minus answers. This therefore means you will be 2 solutions to the quadratic, which makes sense as the graph is a curve and it therefore must cut the x-axis twice.
When the root part is negative(before you find the root) there are no real roots, only complex ones. This means that the curve comes down above the x-axis and doesn’t cut it. If you work out the complex roots, using i for root(-1), your pair of answers will be a conjugate pair.
David Woodfords Quadratic Calculator
This is a console program that i wrote in c++ that will solve a quadratic for you. Just download the file and run it, follow the instructions and it will output the 2 answers for you. I tried to make it work for complex roots as well but somewhere in the decimal data types Ive messed up so only the second parts of the complex answers are correct – though im sure working out -b/2a isn’t too hard for you.
Download quadratic calculator
I think we need to develop a new procedure of creating the quadratic formula that can be applied to create analytical roots of higher polynomials. For example for creating abcde formula of the following polynomial
ax^4 + bx^3 + cx^2 + dx + e = 0
I know what you purpose Mr.Rohedi, by using the new procedure of finding the quadratic formula, you hope can overcome the challenge of finding all roots of Republic Indonesia (RI) Polynomial that recently posted on this address http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=35&start=10, aren’t you?.
I teach people to remember this formula by singing it to the tune of Pop Goes The Weasle.
Hi Dave…I am coming again, but now I need your help to ask mathematicians here. When the quadratic equation is written as x^2+D1*x+D0=0, where D1=b/a and D0=c/a, is there analytic formula for the equal roots in expression of both D1 and D0 but it still be equal to -D1/2 or -b/2a.
Thx Dave…
Denaya Lesa
I have created an extensive article about quadratic formula here:
http://math4allages.wordpress.com/2009/12/18/derivation-of-the-quadratic-formula/
You may want to check it out.
I also observed that you are having a hard time writing equations. You can actully write complex equations in wordpress like
. That is called Latex coding. I have a tutorial here:
http://math4allages.wordpress.com/2009/12/06/latex-tutorial/
Thanks for the link to your article,
As for using LaTex code you will notice that I have begun using this on my more recent posts. When you say you can do this in wordpress you must be referring to wordpress.com site since to use it in wordpress (my installation at least) I needed to install a plugin.
Dave