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Find the values of a for which exactly one root of the equation x^{2}+2 a x+a^{2}-1=0 lies between the numbers 4 and 6.

Option: 1

a\in[1,5]


Option: 2

a\in(1,5)


Option: 3

a\in[-5,-1]


Option: 4

a\in(-7,-3)


Answers (1)

best_answer

If exactly one root of the equation x^{2}+2 a x+a^{2}-1=0 lies between 4 and 6 then, f(4) f(6)<0

\\\left(16+8 a+a^{2}-1\right)\left(36+12 a+a^{2}-1\right)<0 \\ {(a+5)(a+3)(a+7)(a+5)<0} \\ {(a+3)(a+7)(a+5)^{2}<0} \\ (a+7)(a+3)<0

a\in(-7,-3)

Posted by

Ritika Kankaria

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