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 for all x in R So f(x) has exactly one real root in the interval

The sum of all the real roots of equation x^4-3x^3-2x^2-3x+1=0 is

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c 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 cubic polynomial defined by f(x)=x^(3)/(3)+(a-3)x^(2)+x-13. Then the sum of all possible values(s) of a for which f(x) has negative point of local minimum in the interval [ 1,5] is

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+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ^(2). Let n be the numbers of real roots of g(x) =0, then:

Let f(x)=x^3-3x^2+ 3x + 4 , comment on the monotonic behaviour of f(x) at x=0 x=1

Let f(x)=sqrt(x^(2)-4x) and g(x) = 3x . The sum of all values for which f(x) = g(x) is

If f(x) is a real valued polynomial and f (x) = 0 has real and distinct roots, show that the (f'(x)^(2)-f(x)f''(x))=0 can not have real roots.