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Review SYNTHETIC DIVISION to find roots of third degree characteristic polynomial

Review SYNTHETIC DIVISION to find roots of third degree characteristic polynomial. Pamela Leutwyler. (2x – 5)(x + 3)(7x – 2) =. (2x – 5)(x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0. The roots are:. -3. (2x – 5)(x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0. The roots are:.

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Review SYNTHETIC DIVISION to find roots of third degree characteristic polynomial

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  1. Review SYNTHETIC DIVISION to find roots of third degree characteristic polynomial Pamela Leutwyler

  2. (2x – 5)(x + 3)(7x – 2) =

  3. (2x – 5)(x + 3)(7x – 2) = 14x3 + 3x2 – 107x + 30 = 0

  4. The roots are: -3 (2x – 5)(x + 3)(7x – 2) = 14x3 + 3x2 – 107x + 30 = 0

  5. The roots are: -3 (2x – 5)(1x + 3)(7x – 2) = 14x3 + 3x2 – 107x + 30 = 0

  6. The roots are: -3 (2x – 5)(1x + 3)(7x – 2) = 14x3 + 3x2 – 107x + 30 = 0

  7. The roots are: -3 (2x – 5)(1x + 3)(7x – 2) = 14x3 + 3x2 – 107x + 30 = 0 If is a root of the polynomial equation

  8. The roots are: -3 2 7 1 (2x – 5)(1x + 3)(7x – 2) = 14x3 + 3x2 – 107x + 30 = 0 If is a root of the polynomial equation Then qis a factor of 14

  9. 5 2 The roots are: -3 -3 2 7 1 (2x – 5)(1x + 3)(7x – 2) = 14x3 + 3x2 – 107x + 30 = 0 If is a root of the polynomial equation Then qis a factor of 14 andpis a factor of 30

  10. potential rational roots are factors of 14. +1, -1, +2, -2, +7, -7, +14, -14 A characteristic polynomial will always have lead coefficient = 1. Rational eigenvalues will be integral factors of the constant coefficient of the characteristic polynomial . example: find the eigenvalues for the matrix

  11. potential rational roots are factors of 14. +1, -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division:  1 -4 -19 -14

  12. The remainder is NOT ZERO. +1 is not a root. potential rational roots are factors of 14. +1, -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division: +1 1 -4 -19 -14 -3 -22 1 -36 -22 1 -3

  13. The remainder is ZERO. +7 is a root. potential rational roots are factors of 14. +1, -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division: +7 1 -4 -19 -14 21 14 7 0 2 1 3

  14. The remainder is ZERO. +7 is a root. potential rational roots are factors of 14. +1, -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division: +7 1 -4 -19 -14 21 14 7 0 2 1 3 factor this or use quadratic formula or continue with synthetic division to get the other roots.

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