Home
Class 12
MATHS
Consider the polynomial f(x)= 1+2x+3x^2+...

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|`. The real number `s` lies in the interval.
(a) `(- 1/4, 0)`
(b) `(- 11, - 3/4)`
(c) `(- 3/4, - 1/2)`
(d) `(0, 1/4)`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

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 number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0 is :

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

If 3x^(2)+4kx+1 gt 0 for all real values of x, then k lies in the interval

The function f(x)=2log(x-2)-x^2+4x+1 increases on the interval (a) (1,\ 2) (b) (2,\ 3) (c) (1,\ 3) (d) (2,\ 4)

If 4x^(2) + kx + 3 ge 0 for all real values of x then k lies in the interval

The number of distinct real roots of |sinxcosxcosxcosxsinxcosxcosxcosxsinx|=0 in the interval -pi/4lt=xlt=pi/4 is 0 (b) 2 (c) 1 (d) 3

Let f(x)=a x^3+b x^2+c x+d , a!=0 If x_1 and x_2 are the real and distinct roots of f prime(x)=0 then f(x)=0 will have three real and distinct roots if

If -1 +i is a root of x^4 + 4x^3 + 5x^2 + k=0 then its real roots are

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