The set of exhaustive values of a for which the equation `|ax-2|= 2x^2 + ax + 4` has at least one positive root, is

The set of exhaustive values of 'a' for which the inequality (a^(2)+3)x^(2)+(a+2)x-4<2 holds of at least one negative x, is

Complete set of real values of 'a' for which the equation x^4-2ax^2+x+a^2 -a=0 has all its roots real

The set of values of 'a' for which the roots of the equation (a-3)x^(2) - 2ax + 5a = 0 are positive, is

The set of values of 'a' for which the roots of the equation (a-3)x^(2) - 2ax + 5a = 0 are positive, is

Find the least positive value of k for which the equation x^2+k x+4=0 has real roots.

The value of a for which the equation (1-a ^2)x^2+2ax -1 has roots belonging to (0,1) is

The value of 'a' for which the equation ax^(2)-2sqrt(5)x+4=0 has equal roots ,is

The value of 'a' for which the equation x^(3) + ax + 1 = 0 and x^(4) + ax^(2) + 1 =0 has a common root is :