If the roots of the equation x2−2mx+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+m2−1>0, 16−8m+m2−1>0 and -2<m<4 ⇒m2+4m+3>0,m2−8m+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]