SOLUTION: How many positive real zeros does the function f(x) = x4 + x3 – 7x – 1 have? a) 3 or 1 B) 1 c) 2 or 0 d) 0

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Question 534404: How many positive real zeros does the function f(x) = x4 + x3 – 7x – 1 have?
a) 3 or 1
B) 1
c) 2 or 0
d) 0
Answer by fcabanski(1391) About Me  (Show Source):
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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.


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:

+, +, -, - There is one sign change (from + to -), therefore the maximum number of positive real roots is 1 or -1 0r -3 or...


There can't be a negative number of positive real roots. So the answer is 1.


This is Descartes Rule of Signs.