the full-root formula is VERY VERY larger than yours.]]>

i'have been posted it somewhere here.]]>

1/a [ a/2 ± √( a/2 (c/6 - 2√c/3))] and

1/a [ a/2 ± √( a/2 (c/6 + 2√c/3))]

edit*

where of course ax^4 + bx^3 + cx^2 + dx + e = 0

]]>{x -> 0.33000947820757186759866712044837765639971206511454...},

{x -> 0.66999052179242813240133287955162234360028793488546...},

{x -> 0.06943184420297371238802675555359524745213731018514...},

{x -> 0.93056815579702628761197324444640475254786268981486...}

}

Interesting, all four roots are real.]]>

In the end, we have developed technology which allows us to find such roots simply, there really is no need to drone away reinventing the wheel.

If you could find a root to a n'th degree polynomial in O(1) time (constant, not changing based on the values of the equation), then you could greatly speed up many different algorithms, especially for calculators and math software.

It would, indeed, be very useful.

]]>There are other methods out there describing "easier methods" that are derived from the quartic formula, but really they are not that much easier.

You can even use four seesions of Newton's method with differing starting values, but again this is quite time consuming and not as exact as the above methods.

In the end, we have developed technology which allows us to find such roots simply, there really is no need to drone away reinventing the wheel. Maybe the algorithyms would be useful in a world destroyed, or you may just be curious as to how such a computation is possible, and there is nothing wrong with that. But, if you are looking for a reasonable alternative to using technology for this particular purpose, don't waste your time. There are an infinite amount of more important questions to be answered in this universe.

]]>My calculator gives 4 roots between 0 and 1.

]]>i have a equation and i want to show me how can we solve this type of equations ... i get the answers easily from the excel but i want to know how can we solve it in algebra way

70X^4-140X^3+90X^2-20X+1 = o

X = ???

]]>