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7.6 Rational Zero Theorem

7.6 Rational Zero Theorem. Depressed equation. All the possible rational Zeros. To find all the possible rational zero , take all the factors of the last number divide by factors of the lead coefficient. Find all possible rational zero. Find factors of 4: {1, -1, 2, - 2, 4,- 4}

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7.6 Rational Zero Theorem

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  1. 7.6 Rational Zero Theorem Depressed equation

  2. All the possible rational Zeros To find all the possible rational zero , take all the factors of the last number divide by factors of the lead coefficient. Find all possible rational zero. Find factors of 4: {1, -1, 2, - 2, 4,- 4} Find factors of 3 : {1, -1, 3, -3}

  3. All the possible rational Zeros To find all the possible rational zero , take all the factors of the last number divide by factors of the lead coefficient. Find all possible rational zero. Find factors of 4: {1, -1, 2, - 2, 4,- 4} Find factors of 3 : {1, -1, 3, -3} Possible rational zero

  4. How to find all the Rational roots Given the equation: p(x) = x3 – 5x2 – 22x + 56 Possible roots We solve using Synthetic substitution 1 | 1 -5 -22 56

  5. How to find all the Rational roots Possible roots 1 | 1 -5 -22 56 1 -4 -26 1 -4 -26 x Not zero

  6. How to find all the Rational roots Possible roots 2 | 1 -5 -22 56 2 -6 -56 1 -3 -28 0 Zero

  7. How to find all the Rational roots Possible roots 2 | 1 -5 -22 56 2 -6 -56 1 -3 -28 0 Zero “2” Use the depressed equation X2 – 3x – 28 = 0

  8. How to find all the Rational roots Possible roots 2 | 1 -5 -22 56 2 -6 -56 1 -3 -28 0 Zero Use the depressed equation by factoring. X2 – 3x – 28 = 0 ( x – 7)(x + 4) Zero “7, -4” and “2”

  9. Find all the Zeros Possible Roots How many Positive roots are there?

  10. Find all the Zeros Possible Roots How many Positive roots are there? 0 Half the work now.

  11. Find all the Zeros -1 | 1 10 33 38 8 - 1 -9 - 24 -14 1 9 24 14 X Not – 1, reminder is not 0

  12. Find all the Zeros -2 | 1 10 33 38 8 - 2 -16 - 34 -8 1 8 17 4 0 – 2, reminder is 0 Use the depressed equation to find the other zeros Is – 8, still a possible Zero?

  13. Find all the Zeros -2 | 1 10 33 38 8 - 2 -16 - 34 -8 -2 | 1 8 17 4 0 -2 -12 -10 1 6 5 X -2 is a reminder only once

  14. Find all the Zeros -2 | 1 10 33 38 8 - 2 -16 - 34 -8 -4 | 1 8 17 4 0 - 4 -16 - 4 1 4 1 0 • 4 is a Zero !The new depressed equation x2 + 4x + 1= 0

  15. Find all the Zeros Use the Quadratic equation x2 + 4x + 1= 0

  16. Find all the Zeros Use the Quadratic equation x2 + 4x + 1= 0 Answers

  17. Homework Page 381 # 13 – 23 odd 27, 29, 31

  18. Homework Page 381 # 12 – 28 odd 30

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