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Question

Consider f(x)=ax2+bx+c with a>0,
If exactly one root of the quadratic equation f(x)=0 lies between k1 and k2 where k1<k2. The necessary condition for this is:

A
a.f(k2)<0
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B
b2a>k1
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C
f(k1).f(k2)>0
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D
D<0
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Solution

The correct option is B b2a>k1
Let, α,β be the roots of f(x)=ax2+bx+c

Graph for condition, exactly one root of the quadratic equation f(x) lies between k1 and k2.


From graph, required conditions,
(i) b2a>k1
(ii) D>0
(iii) f(k1)f(k2)0

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