Minimum possible number of positive root of the quadratic equation `x^2 -(1 +lambda)x+ lambda -2 =0 ` , `lambda in R`

The values of lambda such that sum of the squares of the roots of the quadratic equation x^(2) + (3 - lambda) x + 2 = lambda has the least value is

The values of lambda such that sum of the squares of the roots of the quadratic equation x^(2) + (3 - lambda) x + 2 = lambda has the least value is

The values of lambda such that sum of the squares of the roots of the quadratic equation x^(2) + (3 - lambda) x + 2 = lambda has the least value is

a and b are the roots of the quadratic equation x^2 + lambdax - 1/(2lambda^(2)) =0 where x is the unknown and lambda is a real parameter. The minimum value of a^(4) + b^(4) is:

The number of real roots of the equation 4x^(3)-x^(2)+lambda^(2)x-mu=0 , mu in R, lambda > 1 is

The value of lambda such that sum of the squares of the roots of the quadratic equation,x^(2)+(3-lambda)x+2=lambda has the least value is

The equation (x^(2)-6x+8)+lambda (x^(2)-4x+3)=0, lambda in R has

If alpha,beta be the roots of the equation 4x^(2)-16x+lambda=0 where lambda in R such that 1

Roots of the equation (x^(2)-4x+3)+lambda(x^(2)-6x+8)=0lambda in R will be