- #1
Saitama
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Homework Statement
Find all the values of 'a', so that exactly one root of the equation x2-2ax+a2-1=0, lies between the numbers 2 and 4, and no root is either equal to 2 or equal to 4.
Homework Equations
The Attempt at a Solution
Let f(x)=x2-2ax+a2-1
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. :)