The function k`f(x)=a x^3+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 ____________.

Let P(x)=x^3-8x^2+c x-d be a polynomial with real coefficients and with all it roots being distinct positive integers. Then number of possible value of c is___________.

If sum of the roots of the equation x^3-3x^2-16x+k=0 is zero then find the value k.

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.

If one root of x^3+2x^2+3x+k=0 is sum of the other two roots then find the value of k

If [a b c1-a] is an idempotent matrix and f(x)=x-^2=b c=1//4 , then the value of 1//f(a) is ______.

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

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

If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then b//a has the value equal to _____.

A function f(x) is such that f(x)=0 has 8 distinct real roots and f(4+x)=f(4-x) for x in R . Sum of real roots of the equation f(x)=0 is