For what values of a does the equation `x^2 + 2asqrt(a^2-3)x + 4 = 0` possess equal 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 m does the equation, mx^(2) + (3x-1)m + 2x + 5 = 0 have equal roots of opposite sign ?

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

For what values of m are the roots of the equation mx^(2) + (m + 3) x + 4 = 0 are equal?

For what value of k, the equation x^(2) + 4kx + 4 = 0 has equal roots?

For what value of m, roots of the equations x^(2) +mx+ 4 =0 are equal?

For what values of k, the equation x^2+2(k-4) x + 2k=0 has equal roots?

For what values of p the quadratic equation 3x^(2) + 12x + 4p = 0 has equal roots?

For what value of k, -2 is a root of the equation 3x^(2)+4x+2k=0 ?