The function k`f(x)=a x^2+b x^2+c x+d` has three positive roots. If the sum of the roots of `f(x)` is 4, the larget possible inegal values of `c//a` is ____________.

If the function f defined as f(x) = (cx)/(2x +3) , x!=-3/2 satisfies f(f(x))=x then find the absolute value of of sum of all possible values of c .

For what value of a, does the function f (x) = x ^(5) - 5x + a has three real roots ?

The equation a x^2+b x+c=0 has real and positive roots. Prove that the roots of the equation a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0 re real and positive.

Let f (x) =x ^(2) +bx+c, minimum value of f (x) is -5, then abosolute value of the difference of the roots of f (x) is :

f(x) is a polynomial function, f: R rarr R, such that f(2x)=f'(x)f''(x). Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

Let f(x)=x^(2)+ax+b, where a,b in R. If f(x)=0 has all its roots imaginary then the roots of f(x)+f'(x)+f(x)=0 are

Let f(x)=x^(2)-bx+c, b is a odd positive integer,f(x)=0 have two prime numbers as roots and b+c=35 Then the global minimum value of f(x) is

If the function f(x) = x^3-9x^2 +24x + c has three real and distinct roots alpha,beta and gamma, then the value of [alpha]+[beta]+[gamma] is