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

alpha,beta are roots of lambda(x^(2)-x)+x+5=0 If lambda1 and lambda2 are the two values of lambda for which the roots alpha,beta are connected by the realation (alpha)/(beta)+(beta)/(alpha)=4 then the value of (((lambda1)/(lambda2)+(lambda2)/(lambda1))/(14)) is:

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 :

the value of lambda for which the line 2x-(8)/(3)lambda y=-3 is a normal to the conic x^(2)+(y^(2))/(4)=1 is:

the value of lambda for which the line 2x-(8)/(3)lambda y=-3 is a normal to the conic x^(2)+(y^(2))/(4)=1 is:

If alpha,beta be the roots of the equation lambda^(2)(x^(2)-x)+2 lambda x+3=0 and 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 equation whose roots are ((lambda_(1))^(2))/(lambda_(2)) and ((lambda_(2))^(2))/(lambda_(1))

If complete set of values of lambda for which |x-1|+|x-2|+|x-3|+|x-4|=lambda has infinitely many solution is {a} , then the value of (1)/(a) is

Find the value of lambda for which equation 3x^(4)-8x^(3)-6x^(2)+24x=lambda has

Find the set of values of lambda for which the equation |x^(2)-4|x|-12]=lambda has 6 distinct real roots.

Find the number of integral values of lambda, for which equation 4cos x+3sin x=2 lambda+1 has a solution.