let `1 + 2x + 3x^2 + 4x^3 + ........ + gt= 4.` If the least value of `x` is `lambda` then `lambda` equals

If lambda be the ratio of the roots of the quadratic equation in x,3m^(2)x^(2)+m(m-4)x+2=0 then the least values of m for which lambda+(1)/(lambda)=1 is

If alpha, beta are the roots of x^2 – 3x + lambda = 0 (lambda in R) and alpha < 1

If lambda is a root of x^(2) + 3x + 1 = 0 then tan^(-1) lambda+ tan^(-1) (1/lambda) is equal to

The equations lambda x -y = 2 ,2 x -3 y = - lambda and 3x - 2y = - 1 are consistent for a) lambda=-4 b) lambda=1,4 c) lambda=1,-4 d) lambda=-1,4

If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negative roots, then the least value of lambda equals__________.

If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negative roots, then the least value of lambda equals__________.

If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negative roots, then the least value of lambda equals__________.

If : f(x) {:( =x+lambda", ... " x lt 3),(=4", ... " x = 3 ),(= 3x-5 ", ... "x gt 3 ):} is continuous at x = 3 , then : lambda

If x - lambda is a factor of x^(4)-lambda x^(3)+2x+6 . Then the value of lambda is