(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For what real values of 'a' do the roots of the equation [itex]x^2-2x-(a^2-1)=0[/itex] lie between the roots of the equation [itex]x^2-2(a+1)x+a(a-1)=0[/itex]

2. Relevant equations

3. The attempt at a solution

The required conditions are

[itex] \large D_1\geq0[/itex]

[itex] \large D_2\geq0[/itex]

[itex] \large R_1<\dfrac{-2}{2}<R_2[/itex]

where

[itex]D_n=[/itex]Discriminant of nth equation and [itex]R_m=[/itex] mth roots of the latter equation

Solving simultaneously the above inequalities and taking intersection

[itex]a\in \left(\frac{-1}{3},0\right)[/itex]

But the correct answer is

[itex]a\in \left(\frac{-1}{4},1\right)[/itex]

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# Homework Help: Roots lying between the roots of a given equation

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