Using Descartes' Rule of Signs (4.6.4) Flashcards
- Rene Descartes (1596 -1650) was significant both to mathematics and to philosophy.
- He developed the Cartesian system with the x- and y-axes used for graphing.
- He developed the rule about possible solutions to functions that is presented here.
- He posed the still quoted “I think, therefore I am” proof of existence for philosophers.
- Rene Descartes (1596 -1650) was significant both to mathematics and to philosophy.
- He developed the Cartesian system with the x- and y-axes used for graphing.
- He developed the rule about possible solutions to functions that is presented here.
- He posed the still quoted “I think, therefore I am” proof of existence for philosophers.
• Descartes’ rule of signs informs us about potential roots:
1. Write the polynomial with the highest degree term first and the others following in descending order.
2. Next, examine the function when +x is substituted. The number of sign changes from one term to the next tells you the
number of positive real roots or that number less some real even number.
3. Finally, look at the function when –x is substituted. The number of sign changes from one term to the next now tells
you the number of negative real roots or that number less some real even number
• Descartes’ rule of signs informs us about potential roots:
1. Write the polynomial with the highest degree term first and the others following in descending order.
2. Next, examine the function when +x is substituted. The number of sign changes from one term to the next tells you the
number of positive real roots or that number less some real even number.
3. Finally, look at the function when –x is substituted. The number of sign changes from one term to the next now tells
you the number of negative real roots or that number less some real even number
• The number of real number zeros that exist is never a negative number.
• The number of real number zeros that exist is never a negative number.
