Determine the possible number of positive real roots for the polynomial . The number of sign changes in the sequence of coefficients is .
Answer & Analysis
Analysis
Question Analysis
This problem evaluates the student's ability to apply Descartes' Rule of Signs to determine the possible number of positive real roots of a polynomial.
Key Concept Explanation
According to Descartes' Rule of Signs, the number of positive real roots is equal to the number of sign changes in the sequence of coefficients, or less than that by a multiple of 2.
Step-by-step Solution
1. Identify the coefficients of the polynomial: 3, -2, 1, -4, 5, -6
2. Count the sign changes in the sequence of coefficients:
From to : 1 change
From to : 1 change
From
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