Solution to the Pentic

[Jon]

The roots to the equation,

ax^5+bx+c=0

are the roots to the quadradic,

((a^2)*(a^2+b^2))x^8 + (a*(b^2)*c)x^4 - ((a^2)*b*c+(b^2)*(a^2+b^2))=0

DEVELOPMENT

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

One plane passes through the origin. The other parallel plane is displaced
by the distance between the two planes. The projection of the curve on one
plane is the same as on the other. However, the plane passing through the
origin cancels x. The projection of the curve on this plane is mapped back
up to the displaced plane and the solution precipitates.

Jon Giffen (c) 2009

[Robert Israel]

Post by Jon
The roots to the equation,
ax^5+bx+c=0
are the roots to the quadradic,
((a^2)*(a^2+b^2))x^8 + (a*(b^2)*c)x^4 - ((a^2)*b*c+(b^2)*(a^2+b^2))=0

Nonsense. Try some examples, e.g. x = 1, a = 1, b = 2, c = 3.

[Robert Israel]

Post by Robert Israel

Post by Jon
The roots to the equation,
ax^5+bx+c=0
are the roots to the quadradic,
((a^2)*(a^2+b^2))x^8 + (a*(b^2)*c)x^4 - ((a^2)*b*c+(b^2)*(a^2+b^2))=0

Nonsense. Try some examples, e.g. x = 1, a = 1, b = 2, c = 3.

Oops, I meant c = -3.