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

Range of values of k for which the point (k,-1) is exterior to both the parabolas y^(2)=|x| is

Range of values of k for which the point (k-1) is exteriro to both the parabolas y^(2)=|x| is

Find the set of values of lambda , for which the point (sqrt(4-lambda^2),lambda) lies outside the triangle formed by the lines (y-3)^2=3x^2 and y+sqrt3=0

If the point (sin theta,(1)/(sqrt(2))) lies exterior to both the parabolas y^(2)=|x| .Then theta can belong to

Find the range of lambda for which equation x^3+x^2-x-1-lambda=0 has 3 real solution.

Is there a real value of lambda for which the image of the point (lambda,lambda-1) by the line mirror 3 x + y = 6 lambda is the point (lambda^2 + 1, lambda) If so find lambda . ,

Is there a real value of lambda for which the image of the point (lambda,lambda-1) by the line mirror 3x+y=6 lambda is the point (lambda^(2)+1,lambda) If so find lambda_(.)

Find the real values of lambda for which the following system of linear equations has non -trivial solutions: x+y-3z=0,( 1+lambda)x+(2+lambda)y-8z=0 , x-(1+lambda)y+(2+lambda)z=0 .

Find the range of lambda for which equation x^(3)+x^(2)-x-1-lambda=0 has 3 real solution.

Find the number of values of lambda for which the system of equations lambdax+y+z=1,x+lambday+z=lambda and x+y+lambdaz=lambda^2 has infinite number of solutions .