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Learning How to Find a Solution

Learning How to Find a Solution. Using Trial and Improvement. Example A solution to the equation. x 3 + 2 x – 5 = 0. Lies between 1 and 2. So try 1.5 first. For 1 mark. Remember we are seeing what happens if x = 1.5. x 3 + 2 x – 5 = 0. (1.5) 3 + 2 (1.5) - 5.

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Learning How to Find a Solution

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  1. Learning How to Find a Solution Using Trial and Improvement

  2. Example A solution to the equation x3 + 2x – 5 = 0 Lies between 1 and 2 So try 1.5 first For 1 mark

  3. Remember we are seeing what happens if x = 1.5 x3 + 2x – 5 = 0 (1.5)3 + 2 (1.5) - 5 Try 1.5 before moving to next slide

  4. Remember x = 1.5 x3 + 2x – 5 = 0 (1.5)3 + 2(1.5) – 5 = Is 1.5 too big or too small? 3.375 + 3 - 5 = 1.375 Compare 1.375 with0 1.375 is bigger than 0 so the value 1.5 is too big! We need to try a smaller value, try 1.4

  5. Try 1.4 before moving on to the next slide Remember we are seeing what happens if x = 1.4 x3 + 2x – 5 = 0 (1.4)3 + 2 (1.4) - 5

  6. 1 mark for trying a 2nd value for x x3 + 2x – 5 = 0 Remember x = 1.4 (1.4)3 + 2(1.4) – 5 = Is 1.4 too big or too small? We need an answer less than 0 2.744 +2.8 - 5 = 0.544 Compare 0.544 with 0 0.544 is bigger than 0 so the value 1.4 is too big! We need to try a smaller value, try 1.3

  7. Try 1.3 before moving on to the next slide Remember we are seeing what happens if x = 1.3 x3 + 2x – 5 = 0 (1.3)3 + 2 (1.3) - 5

  8. 1 mark for finding a + and -ve answer x3 + 2x – 5 = 0 Remember x = 1.3 (1.3)3 + 2(1.3) – 5 = 0 Is 1.3 too big or too small? We need an answer less than 0 2.197 +2.6 - 5 = -0.203 Compare with0 -0.203 is less than 0 so the value 1.3 is too small! The answer is either x = 1.3 or x = 1.4

  9. We halfway between 1.3 and 1.4 need to ty the value 1 mark for trying 1.35 What happens if x = 1.35 Try 1.35 before moving on to the next slide x3 + 2x – 5 = 0 (1.35)3 + 2 (1.35) - 5

  10. So is the answer 1.3 or 1.4 ? 1 mark for answer x3 + 2x – 5 = 0 x = 1.3 or x = 1.4 we are trying 1.35 (1.35)3 + 2(1.35) – 5 Is 1.35 too big or too small? 2.46 + 2.7 - 5 = 0.16 Compare with0 0.16 is bigger than 0 so the value 1.35 is too big The answer is the smaller choice! x = 1.3 to 1dp

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