Question

how factorise quadratic equations?

Answer 1

2X^2 + X -1 =0
The above eq. is an quadratic eq.             
To factorise , e have to split the middle term that is X.So we split X using 2X and X as 2X -X=X .(We have to replace the middle terms by splitting them into 2 which on addition or subtration gives the same old middle term.Note:- The product of the replacing coefficients of the middle term should be equal to the product of the integer with the 1st coefficient and the last number which here is 2 from 2X^2 and -1 .)
2X^2 + X -1 =0
2X^2 +2X - X -1 =0 ............Splitting
2X(X+1) -1(X+1)=0 ............Taking common from 1st 2 terms and last 2 terms each.
(2X-1) (X+1) =0
The product of these 2 is 0 , that means one of them or both are 0 .
either (2X-1)=0 or (X+1)=0
If (2X-1)=0
Then,   X=1/2
If (X+1)=0
Then,   X=-1

So, X= 1/2 or -1
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