Read the follwing passage and answer the...

Read the follwing passage and answer the questions.
Consider the polyomial `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 function `f'(x)` is

A

`(-(1)/(4),0)`

B

`((21)/(64),(11)/(16))`

C

`(9,10)`

D

`(0,(21)/(64))`

Verified by Experts

The correct Answer is:

A

`int_(9)^(1//2)f (x)dx ltint_(0)^(t)f (x)dx ltint_(0)^(3//4)f (x)dx`
Now, `intf(x)dx=int(1+2x+3x^(2)+4x^(3))dx=x+x^(2)+x^(3)+x^(4)`

`impliesint_(0)^(1//2)f(x)dx=15/18gt3/4,int_(0)^(3//4)f(x)dx=530/256lt3`

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