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# The Change of Sign method locates the root of an equation by where it crosses the x-axis.

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Introduction

Method 1: Change of Sign

Change of Sign

The Change of Sign method locates the root of an equation by where it crosses the x-axis. The point at which the curve crosses x-axis is the root. When a function changes sign in a certain interval, we can see that the root, or the place where the curve crosses the axis is within that interval. Using a Decimal Search method, it is possible to find intervals to varying degrees of accuracy to help pinpoint the position of a root.

I am going to use the equation:

Middle

1

-2

1.1

-0.205

1.2

2

1.3

4.645

The above table shows that there is a change of sign between 1.1 and 1.2. Therefore, we now know that the root lies in the interval [1.1,1.2] We can extend the search further to find the interval of the change of sign with greater accuracy.

 x y 1.1 -0.205 1.11 -0.00344 1.12 0.20224 1.13 0.412085

Conclusion

2 (x+1.4) would overlook the second root. As you can see from the graph below, there are two roots; one in the interval [-2,-1] and one in the interval [-1,0]. However, the table only shows one change of sign in the interval [-2,-1].  2.   The Change of Sign Method would also fail with an equation where all of the roots fall within the same interval, such as in the equation y = x3-1.7x2+0.84x-0.108. The table below shows only one change of sign in the interval [0,1]. This would indicate that there is only one root, rather than three, in this interval.  This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

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