Iam trying to solve the following question:
Find all numbers $a$, such that the equation $x^2-ax-a = 0$ has one positive root and one negative root.
I've tried it already but I cannot seem to understand what the question is asking for, so how would I go about solving it? Also how do I find the positive and negative roots of a function in general?
Best Answer
You could use the fact that the product of the two roots is $-a$.
If they have different signs, their product has to be negative. That means $-a<0$.
Also two distinct roots means the discriminant is greater than $0$. This gives you $a^2+4a>0$.
Combining the two should give you the answer.