The number of integral values of m for which the equation `(1+m^(2)) x^(2) - 2(1+3m)x+(1+8m) = 0`, has no real roots is

The number of interal values of m for which the equation (1+m^(2))x^(2)-2(1+3m)x+(1+8m)=0, has no ral roots is

The number of integral values of m for which the quadratic expression (1 + 2m)x^(2) - 2(1 + 3m)x + 4(1 + m), x in R , is always positive is

The number of integral values of m for which the quadratic expression (1 + 2m)x^(2) - 2(1 + 3m)x + 4(1 + m), x in R , is always positive is

The number of integral values of m for which the quadratic expression (1 + 2m)x^(2) - 2(1 + 3m)x + 4(1 + m), x in R , is always positive is

The number of integral values of m for which the quadratic expression (1 + 2m)x^(2) - 2(1 + 3m)x + 4(1 + m), x in R , is always positive is

Absolute sum of integral values of m for which the equation (m^(2)+2m+1)x^(2)-2(m+1)x+(m+1)^(4)-9=0 has rational roots is

Find the values of m for which the equation x^2 -2 (5 + 2m) x+ 3 (7+ 10m) =0 has equal roots.

Find the set of real values of 'm' for which the equation ((x)/(1+x^(2)))^(2)-(m-3)((x)/(1+x^(2)))+m=0 has real roots.

The number of positive integral values of m , m le 16 for which the equation (x^(2) +x+1) ^(2) - (m-3)(x^(2) +x+1) +m=0, has 4 distinct real root is: