Let `f(x) =sqrt((x^2+ax+4)/(x^2+bx+16))` is defined for all real x then find the number of possible ordered pairs (a,b)

If f(x)=sqrt(x^(2)+ax+4) is defined for all x then find the value of a.

If f(x)=sqrt(x^(2)+ax+4) is defined for all x then find the values of a.

Let f(x)=(ax)/(bx+3). where a,b in{y:|y|<6,y~ is~ integer}.~ Then~ write~ the number of possible...ordered pairs (a,b), such that f(f(x)=x

If x^2+ax+b^2=0 has real roots then which of these is a possible ordered pair (a,b) ?

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

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 ?

Let a and b be real numbers such that the function g(x)={{:(,-3ax^(2)-2,x lt 1),(,bx+a^(2),x ge1):} is differentiable for all x in R Then the possible value(s) of a is (are)

Let a and b be real numbers such that the function g(x)={{:(,-3ax^(2)-2,x lt 1),(,bx+a^(2),x ge1):} is differentiable for all x in R Then the possible value(s) of a is (are)