For what values of a does the equation `x^2 - (2^a - 1)x - 3(4^(a-1) 2^(a-2)) = 0` possess real roots?

For what value of a, the equation 3x^2 + 2 (a^2 + 1) x + (a^2 - 3a + 2) = 0 possesses roots of opposite sign?

For what values of a does the equation x^(2)+2a sqrt(a^(2)-3x)+4=0 possess equal roots?

The real values of 'a' for which the quadratic equation 2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0 possess roots of opposite sign is given by:

The sum of integral values of k for which the equations (k-12)x^(2)+2(k-12)x+2=0 possess no real roots is

For what values of 'a' does the quadratic equation x^(2) - ax + 1 = 0 not have real roots ?

Find all real value of a for which the equation x^4 + (a - 1)x^3+ x^2 + (a - 1)x + 1 = 0 possesses at least two distinct positive roots

Find all real value of a for which the equation x^4 + (a - 1)x^3+ x^2 + (a - 1)x + 1 = 0 possesses at least two distinct positive roots

For what values of k does the quadratic equation 4x^(2) - 12x - k =0 have no real roots ?

The real values of 'a' for which the quadratic equation 2x^(2)-(a^(3)+8a-1)x+a^(2)-4a=0 possesses roots of opposite sign is given by