The quadratic equations x2+a2−2x−2a2=0 and x2−3x+2=0 have

Let a be a common root of the equationsx2+a2−2x−2a2=0 and x2−3x+2=0Then,α2+a2−2α−2a2=0 and α2−3α+2=0Now,α2−3α+2=0⇒α=1 ,2Putting α=1 in α2+a2−2α−2a2=0, we get ⇒ a2+1=0, which is not possible for any a∈R.Putting α=2 in α2+a2−2α−2a2=0, we get4+2a2−2−2a2=0, which is true for all a∈R.Thus, the two equations have exactly one common root for all  a∈R.