Originally Posted by

**Danielisew** **Q1: The equation x^3 + 10x = 21**

**has a solution between 1 and 2**

**Use a trial and improvement method to find this solution.**

**Give your answer correct to one decimal place**

**You must show ALL your working.**

We seek a root of $\displaystyle f(x)=x^3+10x-21$ between 1 and 2:

Using the bisection algorithm we get:

Code:

lo f(lo) hi f(hi) mid f(mid)
1 -10 2 7 1.5 -2.625
1.5 -2.625 2 7 1.75 1.859
1.5 -2.625 1.75 1.859 1.625 -0.4589
1.625 -0.4589 1.75 1.859 1.688 0.6804
1.625 -0.4589 1.688 0.680 1.641 -0.1755
1.641 -0.1755 1.688 0.680 1.649 -0.0306
1.649 -0.0306 1.688 0.680 1.653 0.0421
1.649 -0.0306 1.653 0.0421 1.651 0.0103
1.649 -0.0306 1.651 0.0103 1.650 -0.0079
1.650 -0.0079 1.651 0.0103

So to one decimal place the required root is 1.7 (that is the root

is bigger than 1.650 and less than 1.651, all of which round to 1.7

RonL