Learning How to Find a Solution Using Trial and Improvement

Example A solution to the equation x 3 + 2x – 5 = 0 Lies between 1 and 2 So try 1.5 first For 1 mark

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

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

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

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

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

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

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

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