Quadratic Question

**user_5** · March 1st 2010, 01:43 AM

How do I go about answering this question?

Show that the equation $ax^2-(a+b)x+b=0$ has a solution for all values of $a$ and $b$ .

I think I have to use the discriminant, but I'm not sure how.

**sa-ri-ga-ma** · March 1st 2010, 01:53 AM

yes. You are right.
The discriminant is {(a+b)^2 - 4ab} = ....?

**user_5** · March 1st 2010, 02:02 AM

Oh, nevermind I got it now.
$\Delta=(a-b)^2$

Since $(a-b)$ is squared, the answer will always be positive, hence the reason why there are solutions for all values of $a$ and $b$ ?

**sa-ri-ga-ma** · March 1st 2010, 02:11 AM

Originally Posted by user_5

Oh, nevermind I got it now.
$\Delta=(a-b)^2$

Since $(a-b)$ is squared, the answer will always be positive, hence the reason why there are solutions for all values of $a$ and $b$ ?

Yes.

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