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^2-5x + 6|-lambda x+7 lambda=0 has exactly 3 distinct solutions then lambda is equal to

If f(x)=lambda|sinx|+lambda^2|cosx|+g(lambda) has a period = pi/2 then find the value of lambda

If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a root common, then the irrational values of lambda and mu are a lambda=(-3)/4 b. lambda=0 c. mu=3/4 b. mu=0

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mu .

If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 represents an ellipse, then find values of lambdadot

If the lines 3x^(2)-4xy +y^(2) +8x - 2y- 3 = 0 and 2x - 3y +lambda = 0 are concurrent, then the value of lambda is

The system of linear equations x+lambday-z=0 , lambdax-y-z=0 , x+y-lambdaz=0 has a non-trivial solution for : (1) infinitely many values of lambda . (2) exactly one value of lambda . (3) exactly two values of lambda . (4) exactly three values of lambda .

If a circle passes through the point of intersection of the lines x+ y +1=0 and x+ lambda y-3=0 with the coordinate axis, then find the value of lambda .

If x^2-3xy+lambda y^2+3x-5y+2=0 ,represent a pair of straight lines, then the value of lambda is

If lambda x^(2) + 4xy + y^(2) + lambda x + 3y + 2 = 0 represents the equation of the parabola , then the vlaue of lambda is _