English
Hindi

Question

Download Solution PDF

The 2nd approximation to a root of the equation x2 - x - 1 = 0 in the interval (1, 2) by Bisection method will be:

This question was previously asked in
AAI ATC Junior Executive 2018 Official Paper (Shift 1)
Download PDF Attempt in App
View all AAI JE ATC Papers >
  1. 1.75
  2. 1.35
  3. 1.25
  4. 1.5

Answer (Detailed Solution Below)

Option 1 : 1.75
Free Tests
View all Free tests >
Free
AAI ATC JE Physics Mock Test
15 Qs. 15 Marks 15 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

Bisection method:

Used to find the root for a function. Root of a function f(x) = a such that f(a)= 0

Property: if a function f(x) is continuous on the interval [a…b] and sign of f(a) ≠  sign of f(b). There is a value c belongs to [a…b] such that f(c) = 0, means c is a root in between [a….b]

Note:

Bisection method cut the interval into 2 halves and check which half contains a root of the equation.

1) Suppose interval [a…b] .

2) Cut interval in the middle to find m : 

3) sign of f(m) not matches with f(a) proceed the search in the new interval.

Calculation:

Given:

f(x) = x2 - x - 1 = 0  , a = 1 , b = 2

f(1) = 1 - 1 -1 = -1 < 0 , f(2) = 22 - 2 - 1 = 1 > 0 , Hence root lies between 1 and 2

By Bi-section method, 

Which is positive. Hence, the root lies between 1.5 and 2

By Bi-section method, 

The 2nd approximation to a root of the equation x2 - x - 1 = 0 in the interval (1, 2) by Bisection method is 1.75

Download Solution PDF
Latest AAI JE ATC Updates

Last updated on Jul 10, 2025

-> AAI Junior Executive city intimation slip 2025 has been released at the official website. 

-> The AAI ATC Exam 2025 will be conducted on July 14, 2025 for Junior Executive.. 

-> AAI JE ATC recruitment 2025 application form has been released at the official website. The last date to apply for AAI ATC recruitment 2025 is May 24, 2025. 

-> AAI JE ATC 2025 notification is released on April 4, 2025, along with the details of application dates, eligibility, and selection process.

-> A total number of 309 vacancies are announced for the AAI JE ATC 2025 recruitment.

-> This exam is going to be conducted for the post of Junior Executive (Air Traffic Control) in the Airports Authority of India (AAI).

-> The Selection of the candidates is based on the Computer-Based Test, Voice Test and Test for consumption of Psychoactive Substances.

-> The AAI JE ATC Salary 2025 will be in the pay scale of Rs 40,000-3%-1,40,000 (E-1).

-> Candidates can check the AAI JE ATC Previous Year Papers to check the difficulty level of the exam.

-> Applicants can also attend the AAI JE ATC Test Series which helps in the preparation.

Exams Tests Super Practice

More Numerical Solutions of Nonlinear Algebraic Equations Questions

Q1.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q2.The iterative formula to find the root of the equation f(x) = x3 - 5x + 7 = 0 by the Newton Raphson method is ______.
Q3.The iteration step in order to solve for the cube roots of a given number Nusing the Newton- Raphson’s method is
Q4.The real root of x3 + x2 + 3x + 4 = 0 correct to four decimal places, obtained using Newton Raphson method is
Q5.The square root of a number N is to be obtained by applying the Newton Raphson iterations to the equation x2 - N = 0, if i denotes the iteration index, the correct iterative scheme will be
Q6.To solve the equation 2 sin x = x by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration will be closest to
Q7.The Newton-Raphson method is said to have
Q8.If the equation sin (x) = x2 is solved by Newton Raphson’s method with the initial guess of x = 1, then the value of x after 2 iterations would be _______
Q9.During the determination of roots of equations x2 + 2xy = 6 and x2 - y2 = 3 using the Newton-Raphson method, the values of Jacobin matrix ‘D’ is found to be ______. If initial approximation is (1.414, 0.517).
Q10.To find the root of f(x) = 0 by using the bisection method, an iteration is begun with the lower and upper guesses of the root. If xlower and xupper are the roots, then at the end of the iteration, the absolute relative approximate error in the estimated value of the root would be

More Numerical Methods Questions

Q1.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q2.The rate of convergence of Newton Raphson method is :
Q3.If the value of the approximate solution of the initial value problem   \(\rm \left\{\begin{matrix}y'(x)=x(y(x)+1), &x\in R\\\ y(0)=β \end{matrix}\right.\) at x = 0.2 using the forward Euler method with step size 0.1 is 1.02, then the value of β is 
Q4.The iterative formula to find the root of the equation f(x) = x3 - 5x + 7 = 0 by the Newton Raphson method is ______.
Q5.In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to-
Q6.If \(\frac{dy}{dx}\) = x - y2 and y(0) = 1, then y(0.1) correct upto two decimal places (approx.) is:
Q7.In which of the following categories can we put Bisection method?
Q8.Which order of Polynomials can best be integrated using Trapezoidal Rules?
Q9.Consider the differential equation \(\rm \frac{dy}{dx}=4(x+2)-y \) For the initial condition y = 3 at x = 1, the value of 𝑦 at x = 1.4 obtained using Euler’s method with a step-size of 0.2 is _________. (round off to one decimal place)
Q10.Consider the following recursive iteration scheme for different values of variable P with the initial guess x1 = 1. \(x_{n+1}=\frac{1}{2}\left(x_n+\frac{P}{x_n}\right)\), n = 1, 2, 3, 4, 5 For P = 2, x5 is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x5 is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x5 is ________. (round off to three decimal places)
Suggested Test Series
View All >
AAI ATC Junior Executive 2025 Mock Test Series
467 Total Tests with 3 Free Tests
Start Free Test
Vocabulary Master for All Government Exams Mock Test
309 Total Tests with   0 Free Tests
Start Free Test

AAI JE ATC Important Links

ResultCut OffAnswer KeyExam AnalysisAdmit CardEligibility Criteria

More Engineering Mathematics Questions

Q1.If L = {1, 2, 3, 4, 6, 9, 36} is the lattice find the number of complements 9 is having in the below given Hasse diagram?
Q2.Which of the following statements is/are TRUE for undirected graphs?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti master plus teen patti fun teen patti joy