[" Find all values of "alpha" for which the system of inequalities "],[qquad {[x^(2)+2x+alpha<=0],[x^(2)-4x-6 alpha<=0]],[" has a unique solution."]

Find the value of alpha for which roots of equations are equal 4x ^(2) - 20 x + alpha = 0

Let lambda and alpha be real.Find the set of all values of lambda for which the system of linear equations lambda x+(sin alpha)y+(cos alpha)z=0,x+(cos alpha)y+(sin alpha)z=0,quad -x+(sin alpha)y-(cos alpha)z=0

Find all the values of alpha for which the equation sin ^(4) x+ cos^(4)x+ sin 2x +alpha=0 is valid.

Find the values of alpha and beta for which the following system of linear equations has infinite number of solutions: 2x+3y=7,quad 2 alpha x+(alpha+beta)y=28

10/Find the value of alpha and beta for which the following system of linear equations has infinite number of solutions 2x+3y=7,2 alpha x+(alpha+beta)y=28

Find the value of alpha for which the equation (alpha-12)x^(2)+2(alpha-12)x+2=0 has equal roots.

Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation. Find the values of alpha for which Both the roots are equal in magnitude but opposite in sign