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).
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
