A question I stuffed up on the test.........

[gta007]

Hi guys/gals.

Today, I had a test on polynomial functions.
On the test there was a question I couldn't quite figure how to solve correctly. Here it is below.

"Find the value(s) of k for which x^3 + kx - 4x -2k = 0 has three real roots"

I tried using the quadratic formula, but I know that way is wrong as it isn't a quadratic, it's a cubic.
Some of my friends got the answer x<1 which I think is correct, but they just used good ol' 'trial and error' and graphed it on the calculator.

So I was wondering if there was a correct way other than 'trial and error' which would give me the correct answer.

Lucky for me, this was a test and not a SAC. 

[phagist_]

Factorise so you get a quadratic and a linear component.
Then apply the quadratic formula to the quadratic (for 2 solutions)

[Collin Li]

for





Now, use the discriminant to ensure for two solutions.





Note: is the third solution - the one we cancelled out, so that we are left with a quadratic. It exists regardless of what value of is picked.

[gta007]

Thank you phagist_ and coblin for the help.

I did up to the second step, but didn't take out the -1 so both sides would cancel each other out.
Thanks for the help again. Much appreciated.