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jean: thanks. I found that Wiki a bit tough going. On my later post, Lord in comments suggests Descartes' sign rule.

Descartes' rule of sign only gives an estimate on the number of roots, but Sturm theorem gives the exact number (admittedly, this theorem is a bit tricky but it is completely algorithmic)

But after reading the next post, what you need is:
Let k be smaller than n such that n-k is even. Let a_1, a_2, ..., a_k be k real numbers. Then (X-a_1)(X-a_2)...(X-a_k)(X^2+1)^((n-k)/2) is of degree n and a_1, .... , a_k are the only real roots of
this polynomial.
This means that you can craft a polynomial with as many positive roots as the degree.

Did you fix the equation in Wikipedia? If not, you should! Just click the "edit" link in the upper-right hand corner of the relevant section.


"It doesn't matter how much labour or other resources were used in the past to produce this good; if nobody wants it now or is expected to want it in future, it has no value."

Spoken like a true economist. In fact, it does matter. Actually, the expected return at that point is the greatest and the marginal value is therefore at its greatest. This statement is unfortunately so wrong. If you can right this ship, you're bound to be getting somewhere.

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