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1)

Consider the function f(x)=2x33x2x+1     and the  intervals I1=[-1,0],I2= [0,1], I3  =[1,2], I4=[-2,-1]

Then,


A) f(x) =0 has a root in the intervals I1 and I4 only

B) f(x) =0 has a root in the intervals I1 and I2 only

C) f(x) =0 has a root in every interval except in I4

D) f(x)=0 has a root in all the four given intervals

Answer:

Option C

Explanation:

We have,

 f(x)=2x33x2x+1

Let  

  g(x)=x42x3x22+x

 g(1)=12+1121=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)=162842+2=882+2=0

 g(1)= g(2)=0

But  , g(-2)≠ 0

   f(x)=0 has roots in every interval except I4