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Question

# Suppose for fixed real numbers a and b.f(x)=x3+ax2+bx+c, has 3 distinct roots for c =0. Then

A
fc has 3 distinctroots for all real c
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B
fc(x) has 3 distinct roots for all real c>o or for all real c<0, but not for both
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C
fc(x) has 3 distinct roots for all real c in (p,q) for some p<0 and q>0
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D
fc(x) need not have 3 distinct roots for any real c other than zero
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Solution

## The correct option is B fc(x) need not have 3 distinct roots for any real c other than zerof(x)=x3+ax2+bx+cSince f(x) has three roots when c = 0

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