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** $\displaystyle \frac{0}{any \, \, value \, \ne 0} = 0$

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.

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?

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.