- #1

Rubik

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## Homework Statement

Find the critical points where [itex]\alpha[/itex] = 1.

dv/dt = v

^{2}+ [itex]\alpha[/itex]v - u + [itex]\delta[/itex] [I will call this (1)]

du/dt = [itex]\beta[/itex]v - u [call this (2)]

For what values of [itex]\beta[/itex] and [itex]\delta[/itex] are there no critical points?

## Homework Equations

## The Attempt at a Solution

So firstly I set (1) and (2) to = 0 and from (2) I get:

u = [itex]\beta[/itex]v and now I subst. this back into (1)

0 = v

^{2}+ v(1 - [itex]\beta[/itex]) + [itex]\delta[/itex]

Now from the quadratic formula I have this

v = {-(1 - [itex]\beta[/itex]) ± √[(1 - [itex]\beta[/itex])

^{2}- 4[itex]\delta[/itex]]}/2

Now here I am stuck and not sure how to simplify this or interpret this?