The set of possible values of `lambda` for which `x^2-(lambda^2-5 lambda+5)x+(2 lambda^2-3lambda-4)=0` has roots whose sum and product are both less than 1 is

The complete set of possible real values of à for which the equation x^(2)-(lambda^(2)+1)x-4 lambda^(2)=0 has roots whose simm and product both are greater than -1 is

the values of lambda for which (lambda^(2)-3 lambda+2)x^(2)+(lambda^(2)-5 lambda+6)+lambda^(2)-4=0 is identity in x is

The value of lambda for which the equation lambda^2 - 4lambda + 3+ (lambda^2 + lambda -2)x + 6x^2 - 5x^3 =0 will have two roots equal to zero is

The value of lambda for which the equation 2x^(2)-2(2 lambda+1)x+lambda(lambda+1)=0 may have one root less than lambda and other root greater than lambda are given by

The sum of possible value of lambda for which the system of equations (lambda+1)x+8y=4 lambda and lambda x+(lambda+3)y=3 lambda-1 is inconsistent is

The value of (lambda, mu) for which (lambda - mu) x^3 - (lambda - 2) x^2 -3x +7=0 will have two infinite roots is

Find the value of lambda if the equation x^2/(2-lambda)+y^2/(lambda-5)+1=0 represents an ellipse.

The values of lambda for which the function f(x)=lambda x^(3)-2 lambda x^(2)+(lambda+1)x+3 lambda is increasing through out number line (a) lambda in(-3,3)( b) lambda in(-3,0)( c )lambda in(0,3) (d) lambda in(1,3)

The value of lambda in order that the equations 2x^(2)+5 lambda x+2=0 and 4x^(2)+8 lambda x+3=0 have a common root is given by

Out of the two roots of x^(2)+(1-2 lambda)x+(lambda^(2)-lambda-2)=0 one root is greater than 3 and the other root is less than 3 ,then the limits of lambda are