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

Minimum posible number of positive root of the quadratic equation x ^(2) -(1+ lamda) x + lamda -2 =0, lamda in R:

Roots of the quadratic equation (x^2-4x+3)+lamda(x^2-6x+8)=0,lamdainR will be

Find the values of lamda and mu if both the roots of the equation (3lamda+1)x^(2)=(2lamda+3mu)x-3 are infinite.

The values of lamda for which one root of the equation x^2+(1-2lamda)x+(lamda^2-lamda-2)=0 is greater than 3 and the other smaller than 2 are given by

The values of lamda for which one root of the equation x^2+(1-2lamda)x+(lamda^2-lamda-2)=0 is greater than 3 and the other smaller than 2 are given by

If lamda_(1) and lamda_(2) are the two valyes of lamda such that the alpha and beta of quadratic equation lamda(x^(2)-x)+x-5=0 satisfy (alpha)/(beta)+(beta)/(alpha)+(4)/(5)=0 then (lamda_(1))/(lamda_(2)^(2))+(lamda_(2))/(lamda_(1)^(2)) is equal to

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