The value of ‘a’ for which the equation x2-3x+a=0 and x2+ax-3=0 have a common root is

Given equations are x2-3x+a=0    ...(i)and x2+ax-3=0   ...(ii)Subtracting (ii) from (i), we get⇒-3x-ax+a+3=0⇒(a+3)(-x+1)=0⇒either a=-3 or x=1When a=-3, the two equations are identical. So, we take x=1, which is the common root of the two equations. Substituting x=1 in (i), we get 1+a-3=0⇒a=2