discriminant (fraction)

**Punch** · December 6th, 2011, 06:12 PM

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

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

**skeeter** · December 6th, 2011, 06:50 PM

Originally Posted by Punch

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

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

because $\frac{0}{any \, \, value \, \ne 0} = 0$

**TKHunny** · December 6th, 2011, 06:51 PM

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.

**HallsofIvy** · December 7th, 2011, 04:03 AM

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?

**Punch** · December 7th, 2011, 05:54 PM

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.

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