This document discusses the relationship between the roots and coefficients of a quadratic equation. It defines roots as the values that satisfy the equation. The derivation shows that the sum of the roots is equal to the negative of the coefficient of the linear term divided by the coefficient of the quadratic term. The product of the roots is equal to the constant term divided by the coefficient of the quadratic term. An example problem demonstrates how to use these relationships to find the sum and product of roots given a quadratic equation. The document concludes by assigning problems to find the sum and product of roots for several quadratic equations.

1. SUBJECT : MATHEMATICS
CHAPTER ( 2/4 ) : EQUATIONS
LESSON NO : 07 OF 09
TOPIC : RELATIONSHIP
BETWEEN ROOTS AND
COEFFICIENTS OF A
QUADRATIC EQUATION

3. Q. What do you mean by roots?
A. The value of the unknown for which the equality holds
is called the root or solution.
Q. What do you mean by extraneous root?
A. The root for which equality does not hold is known as
extraneous root.
Q. What do you mean by discriminant?
A. The expression “b2  4ac” in Quadratic formula is
known as discriminant.

4. RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION
 Derivation of Roots
 Sum of Roots
 Product of Roots
 Related Example

5. Derivation of Roots
Let ,  be the roots of the Quadratic equation
ax2 + bx + c = 0, where a ≠ 0
then
2a
4acbb 2
 =
2a
4acbb 2
 =
RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION

6. Sum of the Roots
2a
4acbb
2a
4acbb 22



 S
RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION
2a
4acbb4acbb 22

 S
a
b
a
b
S




2
2

a
b
a
b
S




2
2


7. Product of the Roots







 








 

2a
4acbb
2a
4acbb 22
P
RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION
   2
2
22
4
4acbb
a
P

 
 
2
22
4
4
a
acbb
P

 
2
22
4
4
a
acbb
P

 
a
c
a
ac
P  2
4
4

a
c
a
ac
P  2
4
4


8. RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION
Example
If  , are the roots of equation 3 x 2 + 4 x + 5 = 0
then find the value of 2 + 2 ?
Solution
Since ,  are the roots of the given equation
3x2 + 4x + 5 = 0
and
and
a
b

a
c

3
4

3
5


9. Since
2+2 = (+)2 – 2 
By putting the values of  +  and  , we have
2+2













3
5
2
3
4
2
3
10
9
16

9
3016 

9
14

RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION

10. RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION
 Derivation of Root
 Related Example
 Sum of Root
 Product of Root

12. a
b
βα


a
c
αβ 
RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION
Q. What do you mean by
coefficient?
A. A number that serves as a
measure of some property or
characteristics of a body ,material or
process etc.
Q. What is the formula for sum
of the roots?
A The formula for sum of the
roots is
a
b

Q. What is the formula for
product of the roots?
A The formula for product of
the roots is:
a
c


13. Assignment
Find Sum and Product of the Roots of following
(a) x2 – x+ 1 = 0
(b) 2y2 + 5y –1 = 0
(c) 7x2 – 5x + 4 = 0
(d) x2 + 8x + 15 = 0
Assignment
Find Sum and Product of the Roots of following
(a) x2 – x+ 1 = 0
(b) 2y2 + 5y –1 = 0
(c) 7x2 – 5x + 4 = 0
(d) x2 + 8x + 15 = 0
RELATIONSHIP BETWEEN ROOTS AND
COEFFICIENTS OF QUADRATIC EQUATION

14. NEXT:
FORMATION OF A QUADRATIC EQUATION