Write the value of `lambda` for which `x^2+4x+lambda` is a perfect square.

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^2=|x|dot

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^2=|x|dot

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

The value of lambda for which the equation x^2-y^2 - x - lambda y - 2 = 0 represent a pair of straight line, are

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

Write the value of lambda for which the lines (x-3)/(-3)=(y+2)/(2lambda)=(z+4)/2a n d(x+1)/(3lambda)=(y-2)/1=(z+6)/(-5) are perpendicular to each other.

Find the value of lambda so that the line 3x-4y= lambda may touch the circle x^2+y^2-4x-8y-5=0

Find the value of lambda for which the plane x+y+z=sqrt(3)lambda touches the sphere x^2+y^2+z^2-2x-2y-2z=6.

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 value of m for which lambda+(1)/(lambda)=1 , is k-3 sqrt(2) . The value of k is __________.

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