Concept explainers
Using Descartes’ Rule of Signs, we can tell that the polynomial P(x) = x5 − 3x4 + 2x3 − x2 + 8x − 8 has __________, __________, or __________ positive real zeros and __________ negative real zeros.
Use of Descartes’ rule of signs to find out total number of positive and negative real zeros of a polynomial.
Answer to Problem 2E
The polynomial
Explanation of Solution
The given polynomial is,
Definition used: Descartes’ rule of signs tells about the total number of positive and negative roots of a polynomial using sign change.
Find the positive sign variation in given polynomial.
There are 5 sign change in the polynomial, so 5, 3 or 1 are positive real root.
Find the negative sign variation in given polynomial.
As there is no variation sign, that means there is no negative zeros.
The polynomial
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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