Re: roots to 4th, 5th, 6th & 7th degree polynomials
I share your doubts, but if mathematics doesn't forsake me, it has to be
right.
When a curve f(x) crosses the x-axis at point t, for small distances close
to t, the curve approximates a straight line, right? NO, IT DOESN'T.
That's one flaw in my method. If I take the derivative of f(x) at t, the
tangent line is a straight line.
One area is between f(x) and the x-axis from t to (t + delta t), and the
other area is between f(x) and the x-axis from (t - delta t) to t. I simply
say that when f(x) crosses the x-axis at f(x)=0, THE TWO AREAS CANCEL TO
ZERO.
A better strategy is to use the areas above and below the tangent line when
f(x) crosses the x-axis.
g(x) = f '(x) x + b equation of tangent line
INT (f '(x) x + b) dx from (t - delta t) to (t + delta t) = 0
For instance, using the example suggested by Fran
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