Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
Welcome to our Math lesson on Finding the Zeroes of Polynomials through Iterative Methods, this is the seventh lesson of our suite of math lessons covering the topic of The Definition of Monomials and Polynomials, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
We can find the zeroes of higher-order polynomials by applying any of the iterative methods explained in tutorial 9.4. For example, we can use intuition to identify two values of the variable that give numbers with opposite signs as results. Since the given zero of the polynomial lies in that interval, we can narrow it until you obtain the zero of the polynomial to the desired precision. Let's consider an example to clarify this point.
Identify one zero of following polynomial and write it at one decimal place.
Finding the zeroes of a polynomial means solving the equation P(x) = 0. Hence, we have to solve the cubic equation
where the maximum number of zeroes (roots) is 3.
We can begin with a wide range of values, for example, 0 and 5. Thus, for x = 0, we have
and
Since the two values obtained have opposite signs, it is certain that we have a zero for the given polynomial in this range. Thus, combining the change of sign method and the half-interval method, yields
Hence, the zero of the polynomial is between x = 2.5 and x = 5. Yet, for x = 3.75, we have
For x = 3.1 (it is not necessary to use the exact half interval as this gives numbers with many decimal places but we can use values that are close to half of the given interval), we obtain
Again, for x = 3.4, we obtain
Now that we know that the zero of the give polynomial is between 3.1 and 3.4, we check for x = 3.25. Thus,
Hence, the approximate zero of the given polynomial written to one decimal place is x = 3.3, as it is the only option for numbers with one decimal place between 3.25 and 3.4.
Enjoy the "Finding the Zeroes of Polynomials through Iterative Methods" math lesson? People who liked the "The Definition of Monomials and Polynomials lesson found the following resources useful:
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Math tutorial "The Definition of Monomials and Polynomials" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.