Question 534404
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List the signs of the coefficients of each term.  That is, the signs of the numbers in front of the x^n and the constant.  The max number of positive real roots is either the number of sign changes, or the number of sign changes decreased by a multiple of 2.<P>
Make sure the polynomial is written in decreasing order of exponents.  That is ^n , ^(n-1), ^(n-2)...
x^4 + x^3 – 7x – 1  has coefficients 1, 1 -7 -1.  The signs are:<br>
+, +, -, -  There is one sign change (from + to -), therefore the maximum number of positive real roots is 1 or -1 0r -3 or...  <P>
There can't be a negative number of positive real roots.  So the answer is 1.<P>
This is Descartes Rule of Signs.