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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

For the general quartic:

You never see the 4 roots of a quartic given in terms of its coefficients. Here it is:

The roots now are:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

It seems impractical to remember it, but it is a nice formula..

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

It is for reference only. There are numerical means that are superior. I just had fun with the derivation.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

Quartic formula? I thought it was a quadratic formula. Or are they different?

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

Quartic formula is very different, see post #1.

The quadratic formula solves quadratics, the quartic, quartics.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**n872yt3r****Member**- Registered: 2013-01-21
- Posts: 392

Yup. That is way out of the range.

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

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**DeanPemberton****Member**- From: USA
- Registered: 2014-10-30
- Posts: 20
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The formula is very nice, once we start solving the question by using the above formula, then we can easily remember the above formula. Not too difficult to remember the above formula.

It is not easy to remember all this formula, few formula we can remember because there are some formulas which are like some basic formulas which we can use sometimes.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

Hi;

You are not required to memorize it. You can always look it up if necessary. Also, there are other methods to get roots that are more amenable to computation, these should be used when possible.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**iamaditya****Member**- Registered: 2016-11-15
- Posts: 34

Hi, It is an outstanding formula. Though impossible to memorize we can look it up if necessary. I want to know who has derived it and how has it been derived.

And yeah please tell me a similar direct formula to solve cubic equations also. It would be vey helpful to me.

*Last edited by iamaditya (2016-11-30 05:21:52)*

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There is no substitute to hard work

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

Hi;

I want to know who has derived it and how has it been derived.

Lodovico Ferrari is credited with the discovery of the solution to the quartic in 1540.

The derivation given above was done with Mathematicas help.

And yeah please tell me a similar direct formula to solve cubic equations also. It would be vey helpful to me.

One way to solve a cubic is given here. I can not recommend it.

http://www.mathisfunforum.com/search.ph … 214129&p=3 in post #54

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**iamaditya****Member**- Registered: 2016-11-15
- Posts: 34

Bobbym , When I'm clicking on this link it is showing "Your search returned no hits"

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

Hi;

That is weird. I will find it again.

Try this:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**iamaditya****Member**- Registered: 2016-11-15
- Posts: 34

yeah now it is coming

Practice makes a man perfect.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**iamaditya****Member**- Registered: 2016-11-15
- Posts: 34

It would take more than triple the time to solve with these formulas than solving it by factorizing. Lol. Factorization is a much better process

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

Iterative methods are superior but it will require a computer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**iamaditya****Member**- Registered: 2016-11-15
- Posts: 34

Yeah bobbym you are right.

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,414

Yeah bobbym you are right.

Hmmm, I am almost never right.

Did you introduce yourself in Introductions?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**iamaditya****Member**- Registered: 2016-11-15
- Posts: 34

Nope

There is no substitute to hard work

All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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