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At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?
Correct answer is '6'. Can you explain this answer?
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At which approximation do we get an approximate root of equation x3 + ...
Solution to equation x3 + 3x – 1 = 0:
Put x = 0 in f(x).
f(0) = 0 + 0 – 1 = – 1
x = 1
f(1) = 13 + 3 – 1 = 3
The root of equation lies between 0 and 1 as f(0) and f(1) has an opposite sign.
Put x = 0 in f(x).
f(0) = 0 + 0 – 1 = – 1
x = 1
f(1) = 13 + 3 – 1 = 3
The root of equation lies between 0 and 1 as f(0) and f(1) has an opposite sign.
First approximation:
f(x0) = 0.53 + 3 x 0.5 – 1 = 0.625,
As f(x0) is positive, next interval for root is 0 and 0.5.
As f(x0) is positive, next interval for root is 0 and 0.5.
Second Approximation:
f(x1) = 0.253 + 3 x 0.25 – 1 = - 0.234875
As f(x1) is negative, the rest lies between 0.25 and 0.5.
f(x1) = 0.253 + 3 x 0.25 – 1 = - 0.234875
As f(x1) is negative, the rest lies between 0.25 and 0.5.
Third Approximation:
f(x2) = 0.17773, which is positive.
Hence, the root lies between 0.25 of 0.375.
f(x2) = 0.17773, which is positive.
Hence, the root lies between 0.25 of 0.375.
Fourth Approximation:
f(x3) = – 0.03198 (–ve)
f(x3) = – 0.03198 (–ve)
Fifth Approximation:
f(x4) = 0.07186
f(x4) = 0.07186
f(x5) = 0.0197
f(x6) = – 0.006197
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At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?Correct answer is '6'. Can you explain this answer?
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At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?Correct answer is '6'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?Correct answer is '6'. Can you explain this answer?.
At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?Correct answer is '6'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At which approximation do we get an approximate root of equation x3 + 3x – 1 = 0 corrected to 2 decimal places?Correct answer is '6'. Can you explain this answer?.
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