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Find the positive root of the equation x^3 + 2x^2 + 10x – 20 using Regula Falsi method and correct upto 4 decimal places.
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Numerical Analysis Questions and Answers – Regula Falsi Method
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This set of Numerical Analysis Multiple Choice Questions & Answers (MCQs) focuses on “Regula Falsi Method”.
1. The formula used for solving the equation using Regula Falsi method is x = bf(a)−af(b)f(a)−f(b).
a) True
b) False
View Answer
Answer: a
Explanation: Let there be two point a and b between which the root lies.
The slope can be written as
y−f(a)x−a=f(a)−f(b)a−b
let y = f(x) = 0
−f(a)x−a=f(a)−f(b)a−b
Therefore,
x = bf(a)−af(b)f(a)−f(b).
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2. Find the positive root of the equation 3x-cosx-1 using Regula Falsi method and correct upto 4 decimal places.
a) 0.6701
b) 0.5071
c) 0.6071
d) 0.5701
View Answer
Answer: c
Explanation: f(0) = -2
f(1) = 1.459697694
Therefore the root lies between 0 and 1 and
a = 0; f(a) = -2
b = 1; f(b) = 1.459697694
Substituting the values in the formula,
x = bf(a)−af(b)f(a)−f(b),
we get x1=−2−0−2−1.459697694=0.57808519; f(x1) = -0.103254906
Therefore, x1 becomes a to find the next point.
X2=−0.103254906−(0.57808519)(1.459697694)−0.103254906−1.459697694= 0.604952253; f(x2) = -7.67249301*10-3
Therefore, x2 becomes a to find the next point.
X3=(−7.67249301∗10−3−(0.604952253)(1.459697694)(−7.67249301∗10−3)−1.459697694 = 0.607017853; f(x3) = -2.991836798*10-4
Therefore, x3 becomes a to find the next point.
X4=(−2.991836798∗10−4)−(0.607017853)(1.459697694)(−2.991836798∗10−4)−1.459697694 =0.607098383; f(x4) = -1.165728726*10-5
Therefore, x4 becomes a to find the next point.
X5=(−1.165728726∗10−5)−(0.607098383)1.459697694(−1.165728726∗10−5)−1.459697694=0.60710152; f(x5) = -4.54801046*10-7
Therefore x5 becomes a to find the next point.
X6=(−4.54801046∗10−7)−(0.60710152)(1.459697694)(−4.54801046∗10−7)−1.459697694]= 0.607101642
Therefore, the positive root corrected to 4 decimal places is 0.6071.
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