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For a quadratic ax² + bx + c = 0
so we know sum of roots = -b /a
product of roots = c/a
let roots of the eq x² - x - k(2x- 1) ⇒ x² - x - 2kx +k ⇒  x² - (1 - 2k)x +k
be x , y
so given x+ y =  0
so (1 - 2k )
/1 = 0 
⇒ k = 1/2
2 5 2
hw to mark it best...plz tell...?
when any other person will answer you will automatically given the option to mark best
i dnt knw wher's that option?
thank you
First of all you must know that any quadratic equation can be written as : 
Note: This is a very powerful tool. Do remember it. 
X^2 -sx+p -----------------(i) 
where s is the sum of its roots and p is their product. 
On comparing your equation , we get 
As we had only to talk about their sum so 
It is given that s=0 
This means that 2k+1=0 
2 2 2