Final answer:
The Descartes' rule of signs is a mathematical method used to determine the possible number of positive and negative roots of a polynomial function. It involves counting sign changes, determining the degree of the polynomial, finding the possible positive roots, and using the quadratic formula if applicable.
Step-by-step explanation:
The Descartes' rule of signs is a mathematical method used to determine the possible number of positive and negative roots of a polynomial function. Here's how to use the rule:
A) Count sign changes in f(-x)
In this step, you need to evaluate the function f(-x) by substituting -x for x and count the number of sign changes in the coefficients. Each sign change represents a different sign of the corresponding term in the polynomial.
B) Determine the degree of the polynomial
The degree of a polynomial is the highest power of x. It determines the maximum number of possible real roots.
C) Find the possible positive roots
According to the rule, the number of positive roots is equal to the number of sign changes or less by an even number.
D) Use the quadratic formula
If the polynomial is a quadratic equation, you can use the quadratic formula to find the roots.