The value of k  for which one of the roots of x2−x+3k=0  is double of one of the roots of x2−x+k=0  is

Let α  be a root of x2−x+k=0 ,then 2α  is a root of x2−x+3k=0 .Then the equations are α2−α+k=0  ….. ( 1 )and 4α2−2α+3k=0   ….. ( 2 )solve ( 1 ) & ( 2 )we get,⇒  α2−3k+2k=α4k−3k=1−2+4⇒  α2=−k2  and α=k2Now, α2=(α)2⇒−k2=(k2)2⇒ k2+2k=0⇒k=−2 (k not equals to 0)