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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|`.

A

increasing in `(-t,-(1)/(4))` and decreasin in `(-(1)/(4),t)`

B

decreasing in `(-t,-(1)/(4))` and decreasing in `(-(1)/(4),t)`

C

increasing in `(-t,t)`

D

decreasing in `(-t,t)`

Text Solution

Verified by Experts

The correct Answer is:
B
As, `f''(x)=2(12x+3)`
`f'(x)gt0,when x gt-1/4and f'(x)lt0, when x lt-1/4.`
`therefore` It could be shown as
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