In effort to solve ax^5+bx+c=0

[Jon]

This is in effort to solve,

ax^5+bx+c=0

however a flaw in my answer occurs when a = -b

other than that, the evolution of the solution is at my web page,
http://jons-math.bravehost.com/pentic.html

I haven't tested it out.

[Sam Wormley]

Post by Jon
This is in effort to solve,
ax^5+bx+c=0
however a flaw in my answer occurs when a = -b
other than that, the evolution of the solution is at my web page,
http://jons-math.bravehost.com/pentic.html
I haven't tested it out.

http://www.wolframalpha.com/input/?i=ax%5E5%2Bbx%2Bc%3D0+%2C+a%3D-b

[Jon]

N=(a[1],a[2],a[3],...,a[n])
X=(x,x^2,x^3,...,x^n)

N*X+a[0]=0 polynomial

a[1]x[1]+a[2]x[2]+a[3]x[3]+...+a[n]x[n]+a[0]=0
plane

construct an orthogonal basis from N,
j[1]=N/|N|
j[2]=(-a[0]/a[n])i[n]-(-a[0]/|N|^2)N
j[3]=...
j[4]=...
.
.
j[n]=

j[2],j[3],j[4],...,j[n] all lie on the plane and are
mutually orthogonal.

Permutate the couples of j[i] with j[1], project X onto
the resulting planes and solve as with,

http://jons-math.bravehost.com/pentic.html

.

Post by Jon
This is in effort to solve,
ax^5+bx+c=0
however a flaw in my answer occurs when a = -b
other than that, the evolution of the solution is at my web page,
http://jons-math.bravehost.com/pentic.html
I haven't tested it out.

[Frederick Williams]

Post by Jon
This is in effort to solve,
ax^5+bx+c=0
however a flaw in my answer occurs when a = -b
other than that, the evolution of the solution is at my web page,
http://jons-math.bravehost.com/pentic.html
I haven't tested it out.

There's no need to.