# Without solving the equation, find the value of the roots

1. Oct 14, 2013

### BOAS

1. The problem statement, all variables and given/known data

23 - 5x - 4x2 = 0

find ($\alpha$ - $\beta$)2

2. Relevant equations

In previous parts of the question i've calculated $\alpha$ + $\beta$, $\alpha$$\beta$, 1/$\alpha$ + 1/$\beta$ and ($\alpha$+1)($\beta$+1) but I can't think of any rules I know to help me solve the problem.

3. The attempt at a solution

Expanding ($\alpha$ - $\beta$)2

gives

$\alpha$2+$\beta$2 -2$\alpha$$\beta$

But I don't know what I can do with this info.

I'd appreciate a nudge in the right direction!

Thanks

2. Oct 14, 2013

### Office_Shredder

Staff Emeritus
You can write your expression fairly simply in terms of $\alpha+\beta$ and $\alpha \beta$ (from which you can get the final answer according to your part 2)

3. Oct 14, 2013

### Staff: Mentor

$(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta$
You said that you have already calculated $\alpha + \beta$ and $\alpha\beta$.

4. Oct 14, 2013

### BOAS

Gah, I should have seen that.

Thanks!