# discriminant (fraction)

• Dec 6th 2011, 06:12 PM
Punch
discriminant (fraction)
Find the set of values of $\displaystyle a$ for which the equation, $\displaystyle \frac{2x^2-4ax+a^2+8}{(x-a)^2}$ has 2 distinct roots.

While I know that this question can be solved by using $\displaystyle b^2-4ac>0$ using the equation $\displaystyle 2x^2-4ax+a^2+8$, I do not understand why $\displaystyle (x-a)^2$ can be ignored. Why is it that only the top of the fraction is considered?
• Dec 6th 2011, 06:50 PM
skeeter
Re: discriminant (fraction)
Quote:

Originally Posted by Punch
Find the set of values of $\displaystyle a$ for which the equation, $\displaystyle \frac{2x^2-4ax+a^2+8}{(x-a)^2}$ has 2 distinct roots.

While I know that this question can be solved by using $\displaystyle b^2-4ac>0$ using the equation $\displaystyle 2x^2-4ax+a^2+8$, I do not understand why $\displaystyle (x-a)^2$ can be ignored. Why is it that only the top of the fraction is considered?

because $\displaystyle \frac{0}{any \, \, value \, \ne 0} = 0$
• Dec 6th 2011, 06:51 PM
TKHunny
Re: discriminant (fraction)
You may ignore the bottom only at your peril!!

Before I thought I had a solution, I would want to know that x=a does NOT make the numerator vanish.
• Dec 7th 2011, 04:03 AM
HallsofIvy
Re: discriminant (fraction)
However, your basic problem with finding "the set values of a for which the equation has 2 distinct roots" is that you don't has an equation!

What did the problem really say?
• Dec 7th 2011, 05:54 PM
Punch
Re: discriminant (fraction)
Quote:

Originally Posted by HallsofIvy
However, your basic problem with finding "the set values of a for which the equation has 2 distinct roots" is that you don't has an equation!

What did the problem really say?

The equation is as posted in post 1.