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4.4 Notes

4.4 Notes. Descarte’s Rule of Signs. 4.4 Notes. Turn to p. 231 and read Descartes’ Rule of Signs. basically…

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4.4 Notes

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  1. 4.4 Notes Descarte’s Rule of Signs

  2. 4.4 Notes Turn to p. 231 and read Descartes’ Rule of Signs. basically… Descartes’ Rule of Signs – There is a relationship between the number of sign changes in the coefficients of the terms of P(x) and how many positive real roots the polynomial has, and there is a relationship between the number of sign changes in the coefficients of the terms of P(-x) and how many negative real roots the polynomial has.

  3. 4.4 Notes How to use DRS to find the number of possible positive real roots: • Count the number of times the signs of the coefficients of the terms change from positive to negative and vice-versa. • Take this answer and subtract multiples of two from it until you get to one or zero.

  4. 4.4 Notes Example 1: The coefficients are: 1 -5 -4 20 The number of sign changes is 2. So there are 2 or 0 possible positive real roots.

  5. 4.4 Notes How to use DRS to find the number of possible negative real roots: • Evaluate the polynomial at P(-x). • Count the number of times the signs of the coefficients of the terms change from positive to negative and vice-versa. • Take this answer and subtract multiples of two from it until you get to one or zero.

  6. 4.4 Notes Example 2: The coefficients are: 1 -5 5 5 -6 The number of sign changes is 3. So there are 3 or 1 possible negative real roots.

  7. 4.4 Notes Example 3: Find the number of possible positive and negative real roots of The coefficients are: 2 3 -6 6 -8 3 The number of sign changes is 4. So there are 4 or 2 or 0 possible positive real roots.

  8. 4.4 Notes Example 3: The coefficients are: -2 3 6 6 8 3 The number of sign changes is 1. So there is 1 possible negative real root.

  9. 4.4 Notes Turn to p. 233. Answer 7 and 8. Use Descartes’ Rule of Signs to determine the number of possible positive and negative real roots. 7. There are 2 or 0 possible positive real roots and 1 possible negative real root. 8. There is 1 possible positive real root and 2 or 0 possible negative real roots.

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