This document provides key points about quadratic equations: 1) The general form of a quadratic equation is ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. 2) A number α is a root if it satisfies the equation when substituted for x. The roots are the same as the zeroes. 3) The discriminant, D = b2 - 4ac, determines the nature of the roots - positive D means two real roots, zero D means equal real roots, and negative D means no real roots.

1. KAILASH RAI SARASWATI VIDYA MANDIR
BY:- SANJU BABA

2. KEY POINTS FOR A QUADRATIC
EQUATION1. The general form of a quadratic equation is
a, b and c are real numbers and
2. A real number is said to be a root of the
quadratic equation where a≠o if
The zeroes of the quadratic polynomial
and the roots of the corresponding quadratic
equation are the same.
3. Discriminant:- The expression is called
discriminant of the equation and
is usually denoted
by D. Thus discriminant
4. Every quadratic equation has two roots which may
be real , co incident or imaginary
02
=++ cbxax
02
=++ cbxax ( ) ( ) 0
2
=++ cba αα
α
cbxax ++2
02
=++ cbxax
acb 42
−
02
=++ cbxax
acbD 42
−=
0≠a

3. 5. IF and are the roots of the equation
then
and
6. Sum of the roots ,
and product of the roots,
7. Forming quadratic equation, when the
roots and are given:-
8. Nature of roots of
i. If D>0, then roots are real and unequal.
ii. D=0, then the equation has equal and real
roots.
iii. D<0, then the equation has no real roots.
α β 02
=++ cbxax
a
acbb
2
42
−+−
=α a
acbb
2
42
−−−
=β
a
b−
=+ βα
a
c
=αβ
( ) 02
=++− αββα xx
02
=++ cbxax

4. KEEP
LEARNING……………………