Regula false position method approximate the curve of
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Answer:
In mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown, that, in modified form, is still in use. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as "guess and check". Versions of the method predate the advent of algebra and the use of equations.
As an example, consider problem 26 in the Rhind papyrus, which asks for a solution of (written in modern notation) the equation x + x/4 = 15. This is solved by false position.[1] First, guess that x = 4 to obtain, on the left, 4 + 4/4 = 5. This guess is a good choice since it produces an integer value. However, 4 is not the solution of the original equation, as it gives a value which is three times too small. To compensate, multiply x (currently set to 4) by 3 and substitute again to get 12 + 12/4 = 15, verifying that the solution is x = 12.
Modern versions of the technique employ systematic ways of choosing new test values and are concerned with the questions of whether or not an approximation to a solution can be obtained, and if it can, how fast can the approximation be found.
Answer:
Regula false position method is a method to find the position of a root of a polynomial f(x) = 0.
Step-by-step explanation:
The first technique for estimating the approximate numerical value of a real root of the equation f(x) = 0 is the regula-falsi method.
This technique is often referred to as the false position approach. The process used to calculate a polynomial's roots (x).
In this procedure, we assume that f(x₁) and f(x₂) are two points with opposite signs at x₁ and x₂, respectively.
Suppose that f(x₁) 0 and f(x2) > 0.
Consequently, f(x₁)f(x₂) 0 since the solution to the equation f(x) = 0 is between x₁ and x₂.
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