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Question

Let f(x)=x4+3x+1,[2,1] then

A
f has exactly two zeros in [2,1]
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B
f has exactly one zero in [2,1]
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C
f has at least one zero in [2,1]
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D
f has no zero in [2,1]
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Solution

The correct option is A f has exactly one zero in [2,1]
Given, f(x)=x4+3x+1
f(x)=4x3+3, it has imaginary root it means f(x)0
it means it will cut only at once to x axis.
f(2)>0,f(1)<0
So, there exist a root in interval [2,1]

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