The roots of `|(x,a,b,1),(lambda,x,b,1),(lambda,mu,x,1),(lambda,mu,v,1)|=0` are

If the roots of the equation (x^(2) -bx)/(ax - c) = (lambda - 1)/(lambda + 1) are such that alpha + beta =0 , then the value of lambda is :

The system of equations lambda x+(lambda+1)y+(lambda-1)z=0,(lambda+1)x+lambda y+(lambda+z)z=0,(lambda-1)x+(lambda+2)y+lambda z= bas a non-trivial solutions for

Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1) and C(0,2,-1) are collinear.

Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1) and C(0,2,-1) are collinear.

For a,b,in R and a!=0, the equation ax^(2)+bx+c=0 and x^(2)+2x+3=0 have atleast one common root if (a)/(lambda)=(b)/(mu)=(c)/(Psi) where lambda,mu and Psi are positive integers.The least value of (lambda+mu+Psi) is

If alpha , beta are the roots of lambda(x^(2)+x)+x+5 =0 and lambda_(1) , lambda_(2) are the two values of lambda for which alpha , beta are connected by the relation (alpha)/(beta)+(beta)/(alpha) =4, then the value of (lambda_(1))/(lambda_(2))+(lambda_(2))/(lambda_(1)) =

If the two roots of the equation (lambda-1)(x^(2)+x+1)^(2)-(lambda+1)(x^(4)+x^(2)+1)=0 are real and distin then lambda lies in the interval

alpha , beta are roots of the equation lambda(x^(2)-x)+x+5=0. If lambda_1 and lambda_2 are the two values of lambda for which the roots alpha , beta are connected b the relation (alpha )/(beta)+(beta)/(alpha)=4 , then the value of (lambda_1)/(lambda_2)+(lambda_2)/(lambda_1) is :

If |{:(x+3,x+4,x+lambda),(x+4,x+5,x+mu),(x+5,x+6,x+v):}|=0 where lambda,mu,v are in A.P then prove that this is an identity in x.