Derive Quadratic Formula
If you want an explanation on using the formula go to the quadratic formula post (with a downloadable solver)
The quadratic formula,
for the general equation ax2+bx+c=0
can be derived using the method of “completing the square” as follows.
starting with
ax2+bx+c=0
divide through by a
x2+bx/a+c/a=0
take the c part to the other side
x2+bx/a=-c/a
In order to complete the square we need to add half the coefficient of x (that’s b/2a) squared to both sides so we get
x2+bx/a + b2/4a2=-c/a +b2/4a2
Now we can factorise the left into a squared bracket (you can check this by multiplying it back out)
(x + b/2a)2=-c/a +b2/4a2
So if we square root both sides and take b/2a to the other side we have x on its own
x = -b/2a ±√(-c/a +b2/4a2)
Now to get this in the more traditional form we can take out 1/2a (Which means each term in the root is timesed by 4a2) from the square root to put the whole thing over 2a
x = (-b ±√(b2-4ac))/2a
Quadratic Solver
Fill in the boxes for the coefficients below to solve any quadratic equation (is also able to find complex roots)
x+
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Comments Left
Ohh of course your derivation above is the common procedure for quadratic formula. There are another ways to create it. The first way by integration technique as commonly met on the internet, while the second way, he he he..only me that can do it. Do you believe me?
OMG, I am very lucky can discuss with @trevorpythag. Thank’s for this chance.
I ever read the derivation of quadratic formula by integration on
http://ariaturns.wordpress.com/2008/10/21/asal-usul-rumus-abc-cara-lain/
Apologise mr, coz I am sure you don’t understand Indonesian language, so I rocommend you to read the step of formulation only. While for the newest derivation of quadratic formula from me, I am apologise can not post here. Because the new method now in preparing to be submitted to maths journal by my father Mr.Rohedi. Be patient @trevorpythag. But according to explanation Mr.Rohedi for me, the new technique can be generalized to create analytic formula for higher polynomials, such as
ax^3+bx^2+cx+d=0
and etc. See for detail at my address.
Again, thank’s you for your attention,
Denaya Lesa.
thankyou for the link
google translator came in useful as well.
Dave
Hi Dave,
I ever see your blog becomes top clicks on this address:
http://metrostateatheists.wordpress.com/2008/12/16/differential-equations-how-they-relate-to-calculus/
Please visit to the website, and leave some comments..
Denaya Lesa,
Myself and the author of that particular post are somewhat perplexed by the astounding amount of traffic we have received for it. Is their some particular reason you and other find the blog so interesting?
@Metro State Atheists
Maybe before I give my special answer for you, let’s read Eric’s comment about our posts:
%%
Greetings! I posed your problem to a friend of mine and he came up with this. What do you think?
%%
Eric is visitor of oxford maths interview 2009 on http://ardoris.wordpress.com/2008/12/19/oxford-maths-interview-2009/
Happy with you @Metro State Atheists.
Denaya Lesa.
@Metro State Atheists and @Dave
Oh yeah, Denaya forgets to inform you if recently ardoris.wordpress.com becomes top clicks on http://arubi.wordpress.com one of blog at Germany. If you have any spare time, please visit to the website.Thx.
@Metro State Atheists and @Dave
Apologise, Denaya also links your math blogs
http://trevorpythag.wordpress.com/2009/01/28/derive-quadratic-formula/
and
http://metrostateatheists.wordpress.com/2008/12/16/differential-equations-how-they-relate-to-calculus/
to
http://arubi.wordpress.com/2008/12/24/kunjungan-masyarakat-nanoteknologi-indonesia-ke-lembaga-nanoteknologi-jerman/#comment-23
Thx.
Denaya Lesa.
@Dave
Thank’s so much Dave, I’ve just seen the list of top clicks on this wonderful math blog.
Congratulation Dave, your math blog now worldwild.
Happy with you,
Denaya Lesa.
@Dave
Now, Denaya adds your math blog with a new link contains my challenges that have been posted at:
http://totient.wordpress.com/2008/03/19/a-funny-derivation/#comment-21
Denaya hopes the challenge could be inspired all of visitors here. Thx.
Okay Dave,
Your math blog would be interested if Denaya completes with the following link
http://dreamofdestiny.wordpress.com/2008/12/31/pythagorean-triple-part-0/,
that discussed Pythagoras formula and several advanced applications. See also another related link at my address.
See you later,
Denaya Lesa.
Hehehe…
Dave, believes you would be glad with this link that related to application of the quadratic formula, especially for solving ODE.
http://chanheeh.wordpress.com/2008/12/02/two-types-of-quadratic-formula/
My special sallom for you Dave..
Denaya Lesa.
please tell method of factors.how i solve quadratic equation from method of factors
@Zulfiqar
see my post
factorising quadratics
I have created an extensive explanantion about Derivation of the Quadratic Formula here:
http://math4allages.wordpress.com/2009/12/18/derivation-of-the-quadratic-formula/
You may want to check it out.
I would be interested to see alternative methods for deriving it.