Let `f(x) =x^2+ ax + b cos x`, a being an integer and b is a real number. Find the number of orderedpars `(a, b)` for which the equations `f(x)=0 and f(f(x)=0` have the same (non-empty) set ofreal roots.

Let f (x) =x^(2)+ lamda x+ mu cos x, lamda being an integer and mu is a real number. The number of ordered pairs (lamda, mu) for which the equation f(x) =0 and f (f (x))=0 have the same (non empty) set of real roots is:

Let f (x) =x^(2)+ lamda x+ mu cos x, lamda being an integer and mu is a real number. The number of ordered pairs (lamda, mu) for which the equation f(x) =0 and f (f (x))=0 have the same (non empty) set of real roots is:

Let f(x)=x^(2)+kx;k is a real number.The set of values of k for which the equation f(x)=0 and f(f(x))=0 have same real solution set.

Let f(x) = x^3 - 3x + b and g(x) = x^2 + bx - 3 where b is a real number. What is the sum of all possible values of b for which the equations f(x)= 0 and g(x) = 0 have a common root ?

Find the number of real roots of the equation f(x) =x^(3) + 2x^(2) +x +2 =0

Find the number of real roots of the equation f(x) =x^(3) + 2x^(2) +x +2 =0

Find the number of distinct real solutions of the equation f(f(x))=0, where f(x)=x^(2)-1

Let f (x)= x^3 -3x+1. Find the number of different real solution of the equation f (f(x) =0

Let f (x)= x^3 -3x+1. Find the number of different real solution of the equation f (f(x) =0

Let f (x) = x^(2)+10x+20. Find the number of real solution of the equation f (f (f (f(x))))=0