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 distinet real roots of f(x) and let t=|s| . The function f(x) is

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

Consider the polynomial f(x)=1 + 2x + 3x^2 +4x^3 for all x in R So f(x) has exactly one real root in the interval

If f(x)=x^(3)-3x+1, then the number of distinct real roots of the equation f(f(x))=0 is

For a polynomia g(x) with real coefficients, let m_(g) denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by S={(x^(2)-1)^(2)(a_(0)+a_(1)+a_(2)x^(2)+a_(3)x^(3)): a_(0) a_(1), a_(2), a_(3)= RR} For a polynomial f. let f and f denote its first and second order derivties, respectively. Then the minimum possible value of (m_(f')+m_(f")) . where f in S is, ____

Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.

Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.

Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.

Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.

Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.