Some Examples Of Quadratic Equation

Factorisation Of a Quadratic equation:

(NOTE: First check whether the whole quadratic equation is divided by an integer or not)

(a) General Equation Problem

ax2+bx+c=0
(a, b and c can have any value, except that a can't be 0).Now,In order to factorize ax2+bx+c=0 we have to find numbers p and q such that p+q=b and pq=c.

After finding p and q, we split the middle term in the quadratic as px+qx and get desired factors by grouping the terms.

(b) Numeric Problem

4x2+2x-2=0
Now,
2x2+x-1=0
2x2+2x-x-1=0
2x(x+1)-1(x+1)=0
(x+1)(2x-1)=0
(x+1)=0 or (2x-1)=0
x=-1 or x=1/2

Addition Of Two Quadratic Equations:

(NOTE: Be aware about sign)

Ex:1
2x2+3x+6=0
3x2+4x-3=0
5x2+7x+3=0
Ex:2
3x2+6x+9=0
    9x+3=0
3x2+15x+12=0
Subtraction Of Two Quadratic Equations:

(NOTE: Be aware about sign)

Ex:1
3x2-6x+5=0
6x2-2x-6=0
(-)(+)(+)
-3x2-4x+11=0
Ex:2
3x2-6x+5=0
   -2x+6=0
   (+)(-)
3x2-4x-1=0

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