If `lambda=` number of real root of `x^(4)+x^(2)-2=0` then `[cos^(2)((1)/(lambda))]` is equal to

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

The number of real roots of sin(2^(x))cos(2^(x))=(1)/(4)(2^(x)+2^(-x)) is

Let lambda be real. If. The origin and the complex roots of 2z^(2)+2z+lambda=0 form the three vertices b of an equilateral triangle, then (1)/(lambda) is equal to _________

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

If alpha,beta are roots of x^2-x+2lambda=0 and alpha,gamma are roots of 3x^2-10x+27lambda=0 then value of (betagamma)/(lambda) is

If lambda x-by+b^(2)=0 is tangent to the circle x^(2)+y^(2)=ax+by then lambda can be equal to

The value of lambda for which the sum of squares of roots of the equation x^(2)+(3-lambda)x+2=lambda is minimum,then lambda is equal to (a) 2 (b) -1 (c) -3(d)-2

The equation cos^(4)x-(lambda+2)cos^(2)x-(lambda+3)=0 have a real solution if

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