Determine the possible number of negative real roots for the polynomial . First, find the polynomial with the variables replaced by their negatives, .
Answer & Analysis
Analysis
Question Analysis
This problem assesses the understanding of Descartes' Rule of Signs, specifically focusing on the number of sign changes in the sequence of coefficients after substituting into the polynomial to determine the possible number of negative real roots.
Key Concept Explanation
According to Descartes' Rule of Signs, the number of negative real roots of a polynomial is equal to the number of sign changes in the sequence of its coefficients when the variables are replaced by their negatives, or less than that by a multiple of 2.
Step-by-step Solution
1. Write down the polynomial:
2. Substitute into the polynomial:
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