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Question

If the roots of the equation x22mx+m2 -1=0 lie in the interval (-2,4) then

A

-1<m<3

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B

1<m<5

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C

1<m<3

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D

-1<m<5

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Solution

The correct option is A

-1<m<3


If roots ax2+bx+c=0 lie between k1 and k2 then of (k1) > 0, of (k2) > 0 and k1 < b2a < k2
f(-2)>0, f(4) > 0 and -2 <m<4
4+4m+m21>0, 168m+m21>0 and -2<m<4
m2+4m+3>0, m28m+15>0 and -2<m<4
(m+1)(m+3) > 0, (m-3)(m-5) > 0 and -2<m<4
-1<m<3 [combining all]

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