If `altbltcltd` the equation `(x-a)(x-c)+lambda(x-b)(x-d)=0` has real roots for

If a

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 real roots for

If altbltcltd then show that the quadratic equation mu(x-a)(x-c)+lamda(x-b)(x-d)=0 has real roots for all real mu and lamda

If a lt b lt c lt d then f(x) = (x -a) (x-c)+ lambda(x-b) (x-d) has real roots

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 (a) no real roots. (b) one real root between a and c (c) one real root between b and d (d) Irrational roots.

If altbltcltd , then the roots of equation (x-a)(x-c)+2(x-b)(x-d)=0 , are

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 __________.

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

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