1) The document thanks Farooq Sir for providing a wonderful project to work on about quadratics. 2) It was a pleasure and wonderful experience for the author and their team to work on this project. 3) The author thanks all those who helped and motivated them to complete this project.

2. I Would Really Like To Thank Farooq Sir For Giving Such A Wonderful
Project To Work On. It Has Not Only Been A Pleasure But Also A
Wonderful Experience Working On This Project. I Would Like To Extend
My Gratitude To All The People Those Who Helped As Well As Motivated
Me To Make This Project.
THANKYOU ALL
NIKHIL RAVI AND TEAM

3. Definition:
A quadratic function is a function of the
form
f ( x)  ax  bx  c
2
where a, b, c are real numbers and a 
0.
The expression on the right-hand-side
ax  bx  c
2
is call a quadratic expression.

4. A quadratic function is any equation with a
degree* of two.
A quadratic equation is a trinomial** expression
because in standard form it adds three terms
(ax², bx, and c).
*Degree: The highest power of any term of a
polynomial (Algebra to Go).
**Trinomial: A polynomial (the sum of terms) with
three terms (the product of constants and variables)

5. The numbers that satisfy the equation are called
solutions or roots.
The various methods of solving quadratic
equations is :-
• Factorization
• Using the Quadratic Formula

6. Method 1: Factorization
Q. Factorize ax  bx  c
2
If ax  bx  c  (rx  p)( sx  q)
2
then the solutions (roots) of the
equation are
p q
x1   and x2  
r s

7. x  2 x  15  0
2
( x  5)( x  3)  0
x  5, x  3
2x  7x  3  0
2
(2 x  1)( x  3)  0
1
x  3, x 
2

8. METHOD 2: USE THE QUADRATIC
FORMULA
The quadratic formula is often written as
b  b  4ac
2
x
2a
The number b2  4ac is called the
discriminant.

9. Given the quadratic equation
ax  bx  c  0.
2
If :-
b  4ac  0,
2
the equation has real, unequal roots
b  4ac  0,
2
the equation has real, equal roots
b  4ac  0,
2
the equation has complex roots

10. 2x  7x  3  0
2
(7)  (7)  4(2)(3)
2
x
2(2)
7  49  24 7  25 7  5
  
4 4 4
75 75 1
x1   3, x2  
4 4 2

11. x 2  3x  5  0
3  32  4(1)(5)
x
2(1)
3  29

2
3  29 3  29
x1  , x2 
2 2

12. This Project Was Fruitful For Me. I Have Learnt A Lot Of Things Which Will
Benefit Us And Also Help Us In The Future . A Lot Of Things About Quadratics
Has Been Discussed In The Project . The Definition , Types , Ways Of Solving
As Well As Solved Examples . We Surely Hope That You Will Like The Project.