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

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

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

The value of alpha for which the equation (alpha+5)x^(2)-(2 alpha+1)x+(alpha-1)=0 has roots equal in magnitude but opposite in sign,is

The set of values of alpha for which the quadratic equation (alpha + 2) x^(2) - 2 alpha x - alpha = 0 has two roots on the number line symmetrically placed about the point 1 is

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

If alpha and beta are roots of the equation x^(2)+x+1=0 , then alpha^(2)+beta^(2) is equal to

If -1,2,alpha are the roots of the equation 2x^(3)+x^(2)-7x-6=0, then alpha is

If alpha and beta are the roots of the equation x^2+x+1=0 , then alpha^2+beta^2 is equal to: