- #1

tony24810

- 42

- 0

## Homework Statement

Let k be a constant. If α and β are the roots of the equation 3x^2 + 2x - k = 0, find the value of 3α^2 - 2β in terms of k.

## Homework Equations

## The Attempt at a Solution

Obviously, the usual

αβ = -k/3

α + β = -2/3

has been written but I couldn't put them into the equation required despite a full hour's effort.

Also, tried writing (-b+-sqrt(b^2-4ac))/2a, and put respective roots into the equation, it yields something similar to the provided solution, but has an extra root term.

The solution is 4/3 + k.

The latter method gets 4/3 + k + sqrt(4+12k)/6.