Question:medium

If both the roots of the equation \[ x^2-2ax+a^2-1=0 \quad (a\in\mathbb{R}) \] lie in the interval $(-2,2)$, then the equation \[ x^2-(a^2+1)x-(a^2+2)=0 \] has:

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When roots are restricted to an interval, first determine the parameter range, then use sign analysis of the polynomial to locate roots in specific subintervals.

Updated On: Mar 25, 2026

both roots in $(-3,0)$
one root in $(0,2)$ and another root in $(-2,0)$
one root in $(2,3)$ and another root in $(-2,0)$
one root in $(-3,-2)$ and another root in $(0,2)$

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The Correct Option is C

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