Advertisement

QUADRATIC EQUATIONS.

Quadratic Polynomial : a polynomial in the form ax2 + bx + c where a,b,c are real nos. and a is not equal to 0 is called a quadratic polynomial. 

Zeroes of Quadratic Polynomial : The values of the variable as such when substituted, make the LHS value 0 are called zeroes of the polynomial. e.g. -2 and -3 are zeroes of polynomial x2 + 5x + 6. 

Roots of Quadratic Equation : The values of the variable which satisfy the given quadratic equation are called the roots of the quadratic equation. A quadratic equation always has 2 roots. 

Methods of solving Quadratic Equations :
Factorization Method : In this method, product of 1st and 3rd term is taken, and factorized in such a way that its factors are the addition or subtraction of the middle term. Then terms are grouped into twos which are factors of the equation and the inverses of coefficients are the roots of the quadratic equation.
Completing Square Method : In this method,the third term is transferred to the RHS. The LHS is made a perfect square using formula '3rd term = (1/2 coefficient of x)2'. The new third term is added to both sides and then using factorization method roots are calculated.
Formula Method : In this method, a formula is used. The answers are often inverses of one another. The formula is 
x = [-b + square root of(b2 - 4ac)] / 2a. 

Discriminant : When roots are found out by using formula method, the term b2 - 4ac is called the discriminant. It also determines the nature of the roots. 

Relation between roots and coefficients : If p and q are two roots of ax2 + bx + c = 0 then p + q = -b/a and pq = c/a. 

Forming Quadratic Equation from roots : If p and q are two roots, then the Quadratic Equation is x2 - (p + q)x + pq = 0. 

Reducible Equations : Sometimes, a given equation may not be quadratic, but it can be reduced to one. e.g. 5x4 - 22x2 + 8 = 0. Taking x2 = m, we get the equation 5m2 - 22m + 8 = 0.  

PDF FILE TO YOUR EMAIL IMMEDIATELY PURCHASE NOTES & PAPER SOLUTION. @ Rs. 50/- each (GST extra)

SUBJECTS

HINDI ENTIRE PAPER SOLUTION

MARATHI PAPER SOLUTION

SSC MATHS I PAPER SOLUTION

SSC MATHS II PAPER SOLUTION

SSC SCIENCE I PAPER SOLUTION

SSC SCIENCE II PAPER SOLUTION

SSC ENGLISH PAPER SOLUTION

SSC & HSC ENGLISH WRITING SKILL

HSC ACCOUNTS NOTES

HSC OCM NOTES

HSC ECONOMICS NOTES

HSC SECRETARIAL PRACTICE NOTES

2019 Board Paper Solution

HSC ENGLISH SET A 2019 21st February, 2019

HSC ENGLISH SET B 2019 21st February, 2019

HSC ENGLISH SET C 2019 21st February, 2019

HSC ENGLISH SET D 2019 21st February, 2019

SECRETARIAL PRACTICE (S.P) 2019 25th February, 2019

HSC XII PHYSICS 2019 25th February, 2019

CHEMISTRY XII HSC SOLUTION 27th, February, 2019

OCM PAPER SOLUTION 2019 27th, February, 2019

HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019

HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019

SSC ENGLISH STD 10 5TH MARCH, 2019.

HSC XII ACCOUNTS 2019 6th March, 2019

HSC XII BIOLOGY 2019 6TH March, 2019

HSC XII ECONOMICS 9Th March 2019

SSC Maths I March 2019 Solution 10th Standard11th, March, 2019

SSC MATHS II MARCH 2019 SOLUTION 10TH STD.13th March, 2019

SSC SCIENCE I MARCH 2019 SOLUTION 10TH STD. 15th March, 2019.

SSC SCIENCE II MARCH 2019 SOLUTION 10TH STD. 18th March, 2019.

SSC SOCIAL SCIENCE I MARCH 2019 SOLUTION20th March, 2019

SSC SOCIAL SCIENCE II MARCH 2019 SOLUTION, 22nd March, 2019

XII CBSE - BOARD - MARCH - 2019 ENGLISH - QP + SOLUTIONS, 2nd March, 2019

HSC Maharashtra Board Papers 2020

(Std 12th English Medium)

HSC ECONOMICS MARCH 2020

HSC OCM MARCH 2020

HSC ACCOUNTS MARCH 2020

HSC S.P. MARCH 2020

HSC ENGLISH MARCH 2020

HSC HINDI MARCH 2020

HSC MARATHI MARCH 2020

HSC MATHS MARCH 2020


SSC Maharashtra Board Papers 2020

(Std 10th English Medium)

English MARCH 2020

HindI MARCH 2020

Hindi (Composite) MARCH 2020

Marathi MARCH 2020

Mathematics (Paper 1) MARCH 2020

Mathematics (Paper 2) MARCH 2020

Sanskrit MARCH 2020

Sanskrit (Composite) MARCH 2020

Science (Paper 1) MARCH 2020

Science (Paper 2)

Geography Model Set 1 2020-2021


MUST REMEMBER THINGS on the day of Exam

Are you prepared? for English Grammar in Board Exam.

Paper Presentation In Board Exam

How to Score Good Marks in SSC Board Exams

Tips To Score More Than 90% Marks In 12th Board Exam

How to write English exams?

How to prepare for board exam when less time is left

How to memorise what you learn for board exam

No. 1 Simple Hack, you can try out, in preparing for Board Exam

How to Study for CBSE Class 10 Board Exams Subject Wise Tips?

JEE Main 2020 Registration Process – Exam Pattern & Important Dates


NEET UG 2020 Registration Process Exam Pattern & Important Dates

How can One Prepare for two Competitive Exams at the same time?

8 Proven Tips to Handle Anxiety before Exams!

BUY FROM PLAY STORE

DOWNLOAD OUR APP

HOW TO PURCHASE OUR NOTES?

S.P. Important Questions For Board Exam 2022

O.C.M. Important Questions for Board Exam. 2022

Economics Important Questions for Board Exam 2022

Chemistry Important Question Bank for board exam 2022

Physics – Section I- Important Question Bank for Maharashtra Board HSC Examination

Physics – Section II – Science- Important Question Bank for Maharashtra Board HSC 2022 Examination

Important-formula



THANKS