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Question

(af(μ)<0) is the necessary and sufficient condition for a particular real number μ to lie between the roots of a quadratic equation f(x)=0, where f(x)=ax2+bx+c. Again if f(μ1)f(μ2)<0, then exactly one of the roots will lie between μ1 and μ2.
If |b|>|a+c|, then

A
one root of f(x)=0 is positive, the other is negative
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B
exactly one of the roots of f(x)=0 lies in (1,1)
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C
1 lies between the roots of f(x)=0
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D
both the roots of f(x)=0 are less than 1
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Solution

The correct option is B exactly one of the roots of f(x)=0 lies in (1,1)
Given that |b|>|a+c|
Therefore,
b2(a+c)2>0
a+c+b>0 & ab+c<0

Now, f(1)f(1)=(a+b+c)(ab+c)<0
Therefore, exactly one roots of f(x)=0 lies in (1,1).
Ans: B

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