Iterative Methods

To find a root of a quadratic equation accurately, you can use iteration.

Iteration

 Suppose you had a quadratic equation like this and you had to find its root:

You have to rearrange the equation so that only one x value is on the left hand side. Now, some rearrangements of a quadratic equation will not converge to a root, so you would have to rearrange the equation to something different.

Say the equation would be rearranged like below:

The x on the left hand side would be the value of x we need to find, so we can name it xn.
The x on the right hand side is the value of x we use to find the next value of x, so we can name it xn-1.
The equation will then look like this:

The question will sometimes give you a value of x1. If not, you have to input values of x in the original equation and see the value of x where y changes signs.
Here, x1 will be 4. When you find the next value of x, keep on inputting the previous value of x into the formula until the answer rounds to the same number as your previous value (to 3 s.f.).