Learning How to Find a Solution

Using Trial and Improvement

Example

A solution to the equation

x3 + 2x – 5 = 0

Lies between 1 and 2

So try 1.5 first

For 1 mark

x3 + 2x – 5 = 0

Remember we are seeing what happens if x = 1.5

(1.5) 3 + 2 (1.5) - 5

Try 1.5 before moving to next slide

x3 + 2x – 5 = 0(1.5)3 + 2(1.5) – 5 =

Remember x = 1.5

Is 1.5 too big or too small?

3.375 + 3 - 5 = 1.375

Compare 1.375

with 0

1.375 is bigger than 0 so the value 1.5 is too big!

We need to try a smaller value, try 1.4

x3 + 2x – 5 = 0

Remember we are seeing what happens if x = 1.4

(1.4) 3 + 2 (1.4) - 5

Try 1.4 before moving on to the next slide

x3 + 2x – 5 = 0(1.4)3 + 2(1.4) – 5 = Remember x = 1.4

Is 1.4 too big or too small?

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

We need an answer

less than 0

1 mark for trying

a 2nd value for x

x3 + 2x – 5 = 0

Remember we are seeing what happens if x = 1.3

(1.3) 3 + 2 (1.3) - 5

Try 1.3 before moving on to the next slide

x3 + 2x – 5 = 0

(1.3)3 + 2(1.3) – 5 = 0Remember x = 1.3

Is 1.3 too big or too small?

2.197 +2.6 - 5 = -0.203

Compare

with 0

-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

We need an answer

less than 0

1 mark for finding a + and -ve

answer

x3 + 2x – 5 = 0

What happens if x = 1.35

(1.35) 3 + 2 (1.35) - 5

1 mark for trying

1.35

We halfway between1.3 and 1.4

need to ty the value

Try 1.35 before moving on to the next slide

x3 + 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?

2.46 + 2.7 - 5 = 0.16

Compare

with 0

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 1 mark

for answer

So is the answer 1.3 or 1.4 ?