# Homework Help: Quadratic Equation question

1. May 15, 2012

### Saitama

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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).
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. :)

2. May 15, 2012

### hqjb

The quadratic formula simplifies the root to a function of "a", no need to use graphs, I think your right btw (1,5)-{3} is the union of (1,3) and (3,5)

3. May 15, 2012

### I like Serena

Hey Pranav-Arora!

Aha! You're drawing again. Good!

Yep.

Not stuck.
This is indeed another set of inequalities that you also have to solve.
The solution is the combination of both solutions.

4. May 15, 2012

### Saitama

Oh yes, i knew about it, it will reduce to (x-a)2-1=0 and then we can proceed on the next steps. Thanks for the reply! :)

Hello ILS!

Thanks.

Now i understand it. Thanks once again!

5. May 15, 2012

### stef6987

find the square and solve :D