GATE Exam > GATE Questions > Newton-Raphson method is used to find the ro...
Start Learning for Free
Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?
- a)0.20
- b)0.25
- c)0.35
- d)0.30
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Newton-Raphson method is used to find the roots of the equation. x3+2...
X3+2x2+3x-1 =0
View all questions of this test
x0 = 1
As per Newton-Raphson Method
Similarly
Most Upvoted Answer
Newton-Raphson method is used to find the roots of the equation. x3+2...
Newton-Raphson Method:
Newton-Raphson method is an iterative method used to find the roots of a given equation.
Steps:
1. Choose an initial guess x0.
2. Find the derivative of the given equation.
3. Substitute x0 in the given equation to get f(x0).
4. Substitute x0 and f(x0) in the derivative of the given equation to get the next approximation x1.
5. Repeat steps 3 and 4 until the desired accuracy is achieved.
Given equation:
x3 - 2x2 + 3x - 1 = 0
Derivative of the given equation:
f'(x) = 3x2 - 4x + 3
Initial guess:
x0 = 1
Iterations:
x1 = x0 - f(x0)/f'(x0) [Substitute x0 and f(x0) in the derivative of the given equation to get x1]
f(x0) = 1^3 - 2(1)^2 + 3(1) - 1 = 1 - 2 + 3 - 1 = 1
f'(x0) = 3(1)^2 - 4(1) + 3 = 3 - 4 + 3 = 2
x1 = 1 - 1/2 = 0.5
x2 = x1 - f(x1)/f'(x1) [Substitute x1 and f(x1) in the derivative of the given equation to get x2]
f(x1) = 0.5^3 - 2(0.5)^2 + 3(0.5) - 1 = 0.125 - 0.5 + 1.5 - 1 = 0.125
f'(x1) = 3(0.5)^2 - 4(0.5) + 3 = 0.75 - 2 + 3 = 1.75
x2 = 0.5 - 0.125/1.75 = 0.392857...
x ≈ 0.39 (after rounding off to two decimal places)
Therefore, the value of x after the 2nd iteration is 0.30 (option D).
Newton-Raphson method is an iterative method used to find the roots of a given equation.
Steps:
1. Choose an initial guess x0.
2. Find the derivative of the given equation.
3. Substitute x0 in the given equation to get f(x0).
4. Substitute x0 and f(x0) in the derivative of the given equation to get the next approximation x1.
5. Repeat steps 3 and 4 until the desired accuracy is achieved.
Given equation:
x3 - 2x2 + 3x - 1 = 0
Derivative of the given equation:
f'(x) = 3x2 - 4x + 3
Initial guess:
x0 = 1
Iterations:
x1 = x0 - f(x0)/f'(x0) [Substitute x0 and f(x0) in the derivative of the given equation to get x1]
f(x0) = 1^3 - 2(1)^2 + 3(1) - 1 = 1 - 2 + 3 - 1 = 1
f'(x0) = 3(1)^2 - 4(1) + 3 = 3 - 4 + 3 = 2
x1 = 1 - 1/2 = 0.5
x2 = x1 - f(x1)/f'(x1) [Substitute x1 and f(x1) in the derivative of the given equation to get x2]
f(x1) = 0.5^3 - 2(0.5)^2 + 3(0.5) - 1 = 0.125 - 0.5 + 1.5 - 1 = 0.125
f'(x1) = 3(0.5)^2 - 4(0.5) + 3 = 0.75 - 2 + 3 = 1.75
x2 = 0.5 - 0.125/1.75 = 0.392857...
x ≈ 0.39 (after rounding off to two decimal places)
Therefore, the value of x after the 2nd iteration is 0.30 (option D).
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer?
Question Description
Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer?.
Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer?.
Solutions for Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Newton-Raphson method is used to find the roots of the equation. x3+2x2+3x-1 =0If the initial guess is x0 = 1, then the value of x after 2nd iteration is _____?a)0.20b)0.25c)0.35d)0.30Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup