Answer:
Option C
Explanation:
We have,
f(x)=2x3−3x2−x+1
Let
g(x)=x42−x3−x22+x
g(−1)=12+1−12−1=0
and g(0)= 0
∴ f(x)=0 has roots lie in [-1,0]
Similarly , g(0)=g(1)=0
∴ f(x)=0 has roots lie in [0,1].
g(2)=162−8−42+2=8−8−2+2=0
g(1)= g(2)=0
But , g(-2)≠ 0
∴ f(x)=0 has roots in every interval except I4