If `a lt b lt c lt d`, then for any real non-zero `lambda`, the quadratic equation `(x-a)(x-c)+lambda(x-b)(x-d)=0`,has

If a

If a

If a

The least positive integeral value of real lambda so that the equation (x-a)(x-c)(x-e)+lambda (x-b)(x-d)=0, (a gt b gt c gt d gt e) has distinct real roots is __________.

If a, b, c, d in R such that a lt b lt c lt d, then roots of the equation (x-a)(x-c)+2(x=b)(x-d) = 0