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Question

If 3 and 4 lies between the roots of the equation x2+2kx+9=0 then k lies in the interval

A
(,3)
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B
(,258)(3,)
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C
(,258)
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D
(258,)
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Solution

The correct option is C (,258)
Let f(x)=x2+2kx+9, whose roots are α,β
Given: α<3<4<β

Conditions:

(i)f(3)<06k+18<0k<3 (1)

(ii)f(4)<08k+25<0k<258 (2)

From (1),(2), we get
k(,258)

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