Definition and examples of quadratic equation

1. JSS MAHAVIDYAPEETA MYSURU 4
JSS INSTITUTE OF EDUCATION
Sakleshpur 573134
ANUSHA RANI A
B.ED 2nd SEMESTER
REG.NO: ED190306
JSS INSTIUTUTE OF EDUCATION
SAKLESHPUR

4. INTRODUCTION
CONTENT
Definition of quadratic equation
Examples
Hidden quadratic equation
Methods of solution
1. Factorization

5. DEFINITION
 In mathematics, a quadratic equation is a polynomial equation of
the second degree.
 The general form is ax2 + bx + c=0
Where x represents a variable or an unknown and a, b and c are
constants with a≠0.
If a=0??
Then the equation is a linear
equation

6. IMPORTANCE
 The general form is ax2 + bx + c = 0
 The expression on the right hand side ax2+ bx+ c is called as a
quadratic expression.
 The name quadratic comes from quad ,meaning square ,because
the variable gets squared like x2.
A quadratic equation is a trinomial expression.
Why???
Because in standard form it adds three terms
ax2 , bx and c.

7. More examples of quadratic equation
 2x2+ 5x+ c=0
In this one a=2,b=5 c=3.
 x2_ 3x=0
This one is little more tricky; Where is a?
In fact a=1, as we don't usually write “1x2” b= -3 and where is c? well, c=0 is
not shown.
 5x- 3=0
Oops! This one is not be quadratic equation because it is missing x2 (in other
Words if a=0 and that means it cant be quadratic).

8. METHODS OF SOLUTION
The methods of solving quadratic equation is :
• Factorization

9. Ex: Solve x2 + 7x + 6 = 0
Quadratic equation
 factor the left hand side (LHS)
x2 + 7x + 6 = (x + 6 )(x + 1)
 x2 + 7x + 6 = (x + 6)(x + 1) = 0
Now the equation as given is of the form ab = 0
 set each factor equal to 0 and solve
x + 6 = 0 x + 1 = 0
Solution: x = - 6 and – 1  x = {-6, -
1}

10. Method 1: Factorization
Q : Factorize ax2+ bx+ c
If ax2+ bx+ c = (rx + p)(sx + p) = 0
Then the solutions of the equation are
x1 = -p/r x2 = -q/s
Example:
x2 -2x -15=0
(x - 5) (x + 3)=0
x =5 x=-3
-15 x2
-5 +3 2
2

11. Any questions . . .