Find the interval of `alpha` for which `(alpha, alpha^2, alpha) and (3, 2, 1)` lies on same side of `x+y-4z+2=0`.

Find the values of alpha for which the point (alpha-1,alpha+1) lies in the larger segment of the circle x^2+y^2-x-y-6=0 made by the chord whose equation is x+y-2=0

Find the values of alpha for which the point (alpha-1,alpha+1) lies in the larger segment of the circle x^2+y^2-x-y-6=0 made by the chord whose equation is x+y-2=0

Find the set of those value(s) of alpha for which (7-(5alpha)/4,alpha) lies inside the ellipse x^2/25+y^2/16=1

Find the range of (alpha,2+alpha) and ((3alpha)/2,a^2) lie on the opposite sides of the line 2x+3y=6.

Determine all the values of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines. 2x+3y-1=0 x+2y-3=0 5x-6y-1=0

Determine all the values of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines. 2x+3y-1=0 x+2y-3=0 5x-6y-1=0

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.

Statement 1: The value of alpha for which the point (alpha,alpha^2) lies inside the triangle formed by the lines x=0,x+y=2 and 3y=x is (0,1)dot Statement 2: The parabola y=x^2 meets the line x+y=2 at (1,1)dot

Find the values of alpha so that the point P(alpha^2,alpha) lies inside or on the triangle formed by the lines x-5y+6=0,x-3y+2=0 a n d x-2y-3=0.