• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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

Extracts from this document...


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:

...read more.










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.











...read more.


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.



...read more.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Core & Pure Mathematics essays

  1. Marked by a teacher

    The Gradient Function

    5 star(s)

    � - 3x� = 3(x� + 2hx + h�) - 3x� = 3x� + 6hx + 3h� - 3x�= 6hx + 3h� x +h-x h h h = 6x + 3h = 6x axn value gradient function x2 2x 2x2 4x 3x2 6x Here, I have noticed a trend in these data.

  2. Numerical Method of Algebra.

    0.002195576 -0.663 0.004119811 -0.662 0.006036665 -0.661 0.007946179 Tbl DS-04: Step 4 X Y -0.6659 -0.001480948 -0.6658 -0.001286774 -0.6657 -0.001092676 -0.6656 -0.000898652 -0.6655 -0.000704703 -0.6654 -0.000510829 -0.6653 -0.000317029 -0.6652 -0.000123304 -0.6651 7.03455E-05 7.03455E-05 represents Tbl DS-05: Step 5 X Y -0.66519 -0.000103936 -0.66518 -8.45685E-05 -0.66517 -6.52016E-05 -0.66516 -4.58355E-05 -0.66515 -2.64701E-05 -0.66514

  1. Change of Sign Method.

    In this case, using the method of decimal search has caused an incorrect conclusion to be reached. This is because the curve touches the x-axis between x=1 and x=2, therefore there is no change of sign and consequently all change of sign methods are doomed to failure.

  2. The method I am going to use to solve x−3x-1=0 is the Change ...

    The root now is -0.3475 and the maximum error of this root would be 0.0005. The "Change Of Sign" is very effective, however, sometimes the Decimal Search method would not work with some function. An example is 5x^4+x�-2x�-0.1x+0.1=0 . This would not work because the roots are so near.

  1. Finding the root of an equation

    The next part of the investigation is establishing where, between -0.2606 and -0.2605, a change of sign occurs. X Y 0.2606 0.000355557 -0.26059 0.000310821 -0.26058 0.000266086 -0.26057 0.000221351 -0.26056 0.000176616 -0.26055 0.000131882 -0.26054 0.000087148 -0.26053 0.000042414 -0.26052 -0.000002319558 -0.26051 -0.000047053 -0.2605 -0.000091785 There is a change of sign and therefore a root between -0.26053 and -0.26052.

  2. maths pure

    An example of this may be the function f(x) = (x-1)(x+2)2. The graph of f(x) = (x-1)(x+2)2 is illustrated below. As can be seen the curve only touches the point x = -2 and does not cross the x-axis. x = -2 is clearly a root of the function f(x)

  1. Numerical Method (Maths Investigation)

    I only got its range, -0.66514 < root of the equation used < -0.66513. So, I decide to get their error bound by: Average of the upper and lower error bound = = Upper Error Bound = Lower Error Bound = The Error Bound of the root of this equation

  2. Change of Sign Method

    x = -1.77045 � 0.0005 Failure of the Change of Sign Method When an equation has more than one root between two integers not all or none of the roots may be identified using an integer search. For example the equation x3-19x+31=0 has two roots between x=2 and x=3 as shown in the graph of y= x3-19x+31.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work