Re: Quartic equation

In article <1193538261.175196.262380@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, Rob
McDonald <rob.a.mcdonald@xxxxxxxxx> wrote:

I am working a problem which results in a quartic equation of the
form:

ax^4 - bx + c = 0

Due to the physical nature of the problem, only real and positive
solutions of x will have meaning. All coefficients are known to be
positive. No concrete statement about their relative magnitudes can
be made at this time.

Is there a cleaned-up / shortcut form of the quartic formula for this
special case?

Thanks in advance,

Rob

f(x) = ax^4 - bx + c , has at most 2 pos. real roots.
Df = 4ax^3 - b
so relative extrema [min] is at x = x_min = (b/4a)^(1/3)
further x > (b/a)^3 = x_large -> f(x) > 0

so if f(x_min) == 0 there is a double root at x_min
else if f(x_min) > 0 there are no pos. real roots
otherwise there is one in [0,x_min) and one in (x_min,x_large).

does this help??
.

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