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

BOAS

## Homework Statement

23 - 5x - 4x2 = 0

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

## Homework 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.

## 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

Staff Emeritus
Gold Member
2021 Award
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)

Mentor

## Homework Statement

23 - 5x - 4x2 = 0

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

## Homework 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.

## 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

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

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

Gah, I should have seen that.

Thanks!