Home UP BOARD Question Papers NCERT Solutions Sample Papers CBSE Notes NCERT Books CBSE Syllabus

Quadratic Equations Class 10 Notes For Maths Chapter 4

quadratic equations notes for class 10 chapter 4 download pdf , quadratic equations 10 notes, class 10 maths notes, quadratic equations class 10, quadratic equations class 10 notes, class 10 quadratic equations, note maths, maths notes, quadratic equations, class 10 cmaths chapter 4 notes, 10th standard maths notes, 10th std maths notes, class 10 maths notes chapter 4, quadratic equations chapter class 10 notes

NCERT Notes For Mathematis Class 10

Chapter 4:- Quadratic Equations

QUADRATIC EQUATIONS

The polynomial of degree two is called quadratic polynomial and equation corresponding to a quadratic polynomial P(x) is called a quadratic equation in variable x.

Thus, P(x) = ax2 + bx + c =0, a ≠ 0, a, b, c ∈ R is known as the standard form of quadratic equation.

There are two types of quadratic equation.

(i) Complete quadratic equation : The equation ax2 + bx + c 0 where a ≠ 0, b ≠ 0,c ≠ 0
(ii) Pure quadratic equation : An equation in the form of ax2 = 0, a ≠ 0, b = 0, c = 0

ZERO OF A QUADRATIC POLYNOMIAL

The value of x for which the polynomial becomes zero is called zero of a polynomial For instance, 1 is zero of the polynomial x2 — 2x + 1 because it become zero at x = 1.

SOLUTION OF A QUADRATIC EQUATION BY FACTORISATION

A real number x is called a root of the quadratic equation ax2 + bx + c =0, a 0 if aα2 + bα + c =0.In this case, we say x = α is a solution of the quadratic equation.

NOTE :-

1. The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same.

2. Roots of quadratic equation ax2 + bx + c =0 can be found by factorizing it into two linear factors and equating each factor to zero.

SOLUTION OF A QUADRATIC EQUATION BY COMPLETING THE SQUARE

By adding and subtracting a suitable constant, we club the x2 and x terms in the quadratic equation so that they become complete square, and solve for x.

In fact, we can convert any quadratic equation to the form (x + a)2 — b2 = 0 and then we can easily find its roots.

DISCRIMINANT

The expression b2 — 4ac is called the discriminant of the quadratic equation.

SOLUTION OF A QUADRATIC EQUATION BY DISCRIMINANT METHOD

Let quadratic equation is ax2 + bx + c = 0

Step 1.
Find D = b2 — M4ac.

Step 2.
(i) If D > 0, roots are given by x = -b + √D / 2a , -b – √D / 2a
(ii) If D = 0 equation has equal roots and root is given by x = -b / 2a.
(iii) If D < 0, equation has no real roots.

ROOTS OF THE QUADRATIC EQUATION

Let the quadratic equation be ax2 + bx + c = 0 (a ≠ 0).

Thus, if b2 — 4ac ≥ 0, then the roots of the quadratic —b ± √b2 — 4ac / 2a equation are given by

QUADRATIC FORMULA

—b ± √b2 — 4ac / 2a is known as the quadratic formula which is useful for finding the roots of a quadratic equation.

NATURE OF ROOTS

(i) If b2 — 4ac > 0, then the roots are real and distinct.
(ii) If b2 — 4ac = 0, the roots are real and equal or coincident.
(iii) If b2 — 4ac <0, the roots are not real (imaginary roots)

FORMATION OF QUADRATIC EQUATION WHEN TWO ROOTS ARE GIVEN

If α and β are two roots of equation then the required quadratic equation can be formed as x2 — (α + β)x + αβ =0

NOTE :-

Let α and β be two roots of the quadratic equation (ax2 + bx + c = 0 then Sum of Roots: – the coefficient of x / the coefficient t of x2 ⇒ α + β = – b / a

Product of Roots :-

αβ = constant term / the coefficient t of x2 ⇒ αβ = c / a

METHOD OF SOLVING WORD PROBLEMS

Step 1:-

Translating the word problem into Mathematics form (symbolic form) according to the given condition

Step 2 :- Form the word problem into Quadratic equations and solve them.

Quadratic Equations Notes for Class 10

Important Links

NCERT CBSE Notes Class 6 - 12 Download pdf

Ncert Solution for class 6 to 12 download in pdf

CBSE Model test papars Download in pdf

NCERT Books for Class 1- 12 Hindi & English Medium

Mathematics Biology Psychology
Chemistry English Economics
Sociology Hindi Business Studies
Geography Science Political Science
Statistics Physics Accountancy

CBSE Syllabus Class 9 to 12 Year 2021-22

Last year CBSE Question paper

Important Links

Follow Us On

Face book page ncerthelp twitter page youtube page linkdin page

Solved Last Year Question Paper

If You have any problem/query related to above page please send us your Query to ncerthelp@gmail.com with code Serial No1695/1091. Thanks

Please Share this webpage on facebook, whatsapp, linkdin and twitter.

Facebook Twitter whatsapp Linkdin

Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.