•  
agra,ahmedabad,ajmer,akola,aligarh,ambala,amravati,amritsar,aurangabad,ayodhya,bangalore,bareilly,bathinda,bhagalpur,bhilai,bhiwani,bhopal,bhubaneswar,bikaner,bilaspur,bokaro,chandigarh,chennai,coimbatore,cuttack,dehradun,delhi ncr,dhanbad,dibrugarh,durgapur,faridabad,ferozpur,gandhinagar,gaya,ghaziabad,goa,gorakhpur,greater noida,gurugram,guwahati,gwalior,haldwani,haridwar,hisar,hyderabad,indore,jabalpur,jaipur,jalandhar,jammu,jamshedpur,jhansi,jodhpur,jorhat,kaithal,kanpur,karimnagar,karnal,kashipur,khammam,kharagpur,kochi,kolhapur,kolkata,kota,kottayam,kozhikode,kurnool,kurukshetra,latur,lucknow,ludhiana,madurai,mangaluru,mathura,meerut,moradabad,mumbai,muzaffarpur,mysore,nagpur,nanded,narnaul,nashik,nellore,noida,palwal,panchkula,panipat,pathankot,patiala,patna,prayagraj,puducherry,pune,raipur,rajahmundry,ranchi,rewa,rewari,rohtak,rudrapur,saharanpur,salem,secunderabad,silchar,siliguri,sirsa,solapur,sri-ganganagar,srinagar,surat,thrissur,tinsukia,tiruchirapalli,tirupati,trivandrum,udaipur,udhampur,ujjain,vadodara,vapi,varanasi,vellore,vijayawada,visakhapatnam,warangal,yamuna-nagar
Bisection Method

Bisection Method 

Definition:

In mathematics, the bisection method is an easy way to obtain numerical solutions for an equation with a single unknown. For example, if you find yourself stuck for the solution of the transcendental equation, you can always resort to the bisection method for the solution. The bisection method or the Bolzano theorem is utilized to find the roots of any polynomial equation. Roots in mathematics mean the numeric value which, when substituted in the equation in place of the variable, satisfies it or makes the equation zero. Other names of this method in the mathematics world are ‘the binary search method’, ‘the interval halving method’, and ‘the dichotomy method’.

The basics of this method go back to the intermediate value theorem. This method is extremely accurate, robust, and straightforward to use. In this method, the interval or distance between the points is considered a line segment. For analyzing the root, the line segment is bisected or cut into two halves. These are known as subintervals.

Further, the roots are analyzed inside these subintervals, which makes the guessing easy. The actual solution is either on the left of the bisection or right to it. This method splits the interval repeatedly in proportion and replaces a centre point to break the root.

Bolzano Theorem:

Bolzano theorem states that if there exists an interval (x, y) and the dot product of the functions of both the intervals is less than zero (f (x). f (y) < 0), and there exists a function f(a) which is continuous, then there prevails a value ‘z’ which belongs in between the interval (x, y) such that the function of ‘z’, f(z) = 0. Please note that the bisection method works only when the function between the intervals is continuous. The Bolzano theorem is also known as the Bisection Method formula.

By applying the bisection method formula, the z value of the f(z) function that passes through the x-axis is solved for the issues of the bisection method. In this example, the value z is the root of the function f. (z). The value of the tolerance we have chosen for the algorithm defines the value in this bisection method program where c reaches the true root.

Bisection Method Procedure

To solve any problem related to the bisection method or the problem where a continuous transcendental equation is given, follow the steps mentioned below:

  • Find out two distinct points and name them x and y in a way that x is smaller than y and the value of their functions is less than 0. (f(a)* f(b) < 0, Bolzano Theorem)
  • Next, determine the middle point of the line segment or interval (x, y), say ‘z.’
  • z will be the root of the function if and only if f(z) = 0; if not the root, follow the steps further.
  • Now we need to further divide the interval. If f(z) x f(x) <0, there exists a root or solution between z and x, else if f(z) x f (y) < 0, the root will exist between y and z.
  • Carry on these steps until you get f(z) = 0.

Aakashians JEE Topper

Aakashians NEET UG 2023 Champions Again

Historic Results 2023 Aakashians Qualified +1 Lakh

JEE Advanced 2023

JEE Advanced 2023 Stats

JEE Advanced 2022 Topper

NEET Related Links

NEET Exam 2024

NEET 2024 Exam Dates

NEET 2024 Exam pattern

NEET 2024 Syllabus

NEET 2024 Eligibility Criteria

NEET 2024 Application

NEET UG Counselling

NEET FAQ

NEET UG Result

NEET 2024 Cut Off

Neet 2023 Toppers List Names & Rank

Neet Result 2023 Toppers list rank cut off

Neet Answer key Live Download PDF

Neet 2023 State Toppers List

JEE MAIN Related Links

JEE Main 2024

JEE Main Rank Predictor 2024

JEE Main College Predictor 2024

JEE Main 2024 Exam Dates

JEE Main 2024 Exam pattern

JEE Main 2024 Application

JEE Main 2024 Eligibility Criteria

JEE Main 2024 Syllabus

JEE Main 2024 Physics Syllabus

JEE Main 2024 Maths Syllabus

JEE Main 2024 Chemistry Syllabus

JEE Main 2024 Admit Card

JEE Main 2024 Counselling

JEE Main marks vs rank vs percentile

JEE Advanced Result 2023 live topper list

JEE Exam Preparation - How to calculate your rank jee

JEE Maths Syllabus - Important topics and weightage

JEE Advanced Related Links

JEE Advanced 2024 Exam Dates

JEE Advanced 2024 Application

JEE Advanced 2024 Eligibility Criteria

JEE Advanced 2024 Syllabus

JEE Advanced 2024 Maths Syllabus

JEE Advanced 2024 Physics Syllabus

JEE Advanced 2024 Chemistry Syllabus

JEE Advanced Exam Result

JEE Advanced Exam Dates

JEE Advanced Registration Dates

CUET Related Links

CUET 2024 Eligibility Criteria

CUET 2024 Admit Card

CUET 2024 Exam Pattern

CUET 2024 FAQs

CUET 2024 Counselling

CUET 2024 Syllabus

CUET 2024 Result

CUET 2024 Answer Key

CUET 2024 Preparation

CUET CUTOFF

CUET 2024 Application Form

Talk to our expert
Resend OTP Timer =
By submitting up, I agree to receive all the Whatsapp communication on my registered number and Aakash terms and conditions and privacy policy