The sum of all real values of 'm' for which the polynomial `f(x)={x^(2)-2mx-4(m^(2)+1)} {x^(2)-4x-2m(m^(2)+1)}` has exactly three distinct real linear factors is

The sum of all real values of x satisfying the equation (x^(2) -5x+5)^(x^(2)+4x-45)=1 is :

The sum of all real values of X satisfying the equation (x^2-5x+5)^(x^2 + 4x -60) = 1 is:

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:

Determine all real values of the parameter 'a' for which the equation 16x^4 - ax^3 + (2a + 17) x^2 - ax + 16 = 0 has exactly four distinct real roots that form a geometric progression.

Find the sum of all real values of X satisfying the equation (x^2-5x+5)^(x^2 + 4x -60) = 1 .

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 no. of possible integral values of m for which the circle x^2+y^2=4 and x^2+y^2-6x-8y+m^2=0 has exactly two common tangents are

The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2) + 2 (4p^(2) - 1) x + 4(2p^(2)+1) for real values of p and x is

Consider the polynomial f(x)=1 + 2x + 3x^2 +4x^3 for all x in R So f(x) has exactly one real root in the interval

The comlete set of values of m for which the inequality (x ^(2) -mx-2)/( x ^(2) + mx +4)gt-1 is satisfied aa x in R, is :