A band can play as much as 8 minutes of music in a competition. If the band plays a 2.33 minute song and a 4.25 minute song, how
1 answer:
You might be interested in
Descartes' Rule of Signs: A polynomial has no more positive roots than it has sign changes.
A corollary to the Rule of Signs: A polynomial P has no more negative roots than P(–x) has sign changes.
The Fundamental Theorem of Algebra: Any polynomial of degree n has n roots.
The Descartes' Rule of Signs gives you the possible number of positive roots (the possible number of the positive roots of a polynomial is equal to the number of sign changes in the coefficients of the terms or less than the sign changes by a multiple of 2) and corollary to the Rule of Signs gives the possible number of negative roots. Subtracting the sum of these two numbers from the degree of polynomial, you can count the number of complex roots.
Examples:
1. The polynomial has three sign changes but just one positive root (of multiplicity 3) at x = 1
2. The polynomial has two sign changes but no positive roots. On the other hand,
has one sign change and g(x) has one negative root. Therefore, this polynomial has 3-1=2 complex roots (using the Fundamental Theorem of Algebra).