The values of 'a' for which the equation `(x^2 + x + 2)^2 - ( a-3)( x^2+ x+2)(x^2 +x + 1) + (a-4)(x^2 + x + 1)^2 = 0` has atlesast one real root is:

The values of 'a' for which the equation (x^(2)+x+2)^(2)-(a-3)(x^(2)+x+2)(x^(2)+x+1)+(a-4)(x^(2)+x+1)^(2)= has atlesast one real root is:

Find the values of a for which the equation (x^(2)+4x+7)^(2)-(a-2)(x^(2)+4x+6)+(a-3)(x^(2)+4x+6)^(2)=0 has atleast one real root

The number of real roots of the equation (x - 1)^(2) + (x -2)^(2) + (x - 3)^(2) = 0 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:

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:

Is there any real value of ' a ' for which the equation x^2+2x+(a^2+1)=0 has real roots?

Is there any real value of 'a' for which the equation x^(2)+2x+(a^(2)+1)=0 has real roots?