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

Find all the values of 'a', so that exactly one root of the equation x^{2}-2ax+a^{2}-1=0, lies between the numbers 2 and 4, and no root is either equal to 2 or equal to 4.

2. Relevant equations

3. The attempt at a solution

Let f(x)=x^{2}-2ax+a^{2}-1

I tried to visualize the question by graph. The graph could have been like this (this is only a rough sketch):-

From here, i get three inequalities,

f(2)<0 and f(4)>0 and D>0

Solving these inequalities, i get a can lie in interval (1,3).

But this is not the answer, the answer is (1,5)-{3}.

Then i thought that graph could be also like this:-

But this gives completely different set of inequalities, now i am completely stuck.

Any help is appreciated. :)

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# Homework Help: Quadratic Equation question

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