The intergral value of `lamda` for which the expression `x^2-lamdax+(1-2lambda^2)>0,AAx in R` is

The least integral value of lambda for which the expression (lambdax^(2)-4x+3lambda+1) is positive for all x in R,is

The least integral value of lambda for which the expression (lambdax^(2)-4x+3lambda+1) is positive for all x in R,is

If lambda_(1) and lambda_(2) be two values of lambda for which the expression x^(2)+(2-lambda) x+lambda-(3)/(4) becomes a perfect square, then calculate the value of (lambda_(1)^(2)+lambda_(2)^(2)) .

Let lambda_(1),lambda_(2) be two values of lambda for which the expression x^(2)+(2-lambda)x+lambda-(3)/(4) becomes a perfect square.The value of (lambda_(1)^(2)+lambda_(2)^(2)) equals (i) 8 (ii) 25 (ii) 50 (iv) 100

The number of negative intergral values of m for which the expression x ^(2) + 2(m -1) x +m +5 is positive AA x gt 1 is:

The number of negative intergral values of m for which the expression x ^(2) + 2(m -1) x +m +5 is positive AA x gt 1 is:

If lambda_(1),lambda_(2)(lambda_(1)>lambda_(2)) are two values of lambda for which the expression f(x,y)=x^(2)+lambda xy+y^(2)-5x-7y+6 can be resolved as a product of two linear factors, then the value of 3 lambda_(1)+2 lambda_(2) is

The sum of all intergral values of lamda for which (lamda^(2) + lamda -2) x ^(2) + (lamda +2) x lt 1 AA x in R, is:

The sum of all intergral values of lamda for which (lamda^(2) + lamda -2) x ^(2) + (lamda +2) x lt 1 AA x in R, is: