Hi, sorry if this is in the wrong forums not really sure

but here it goes..

The quadratic equation $\displaystyle 2x^2+4x+3=0$ has roots $\displaystyle \alpha$ and $\displaystyle \beta$ .

Find the value $\displaystyle \alpha^4+\beta^4$

Ive managed to expand to $\displaystyle \alpha^4+\beta^4=(\alpha+\beta)^4-4\alpha^3\beta-6\alpha^2\beta^2-4\alpha\beta^3$

but im not sure how to put in terms of $\displaystyle \alpha\beta$ and $\displaystyle \alpha+\beta$ to work out an answer.

Also the previous part of the question asks to show $\displaystyle \alpha^2+\beta^2=1$ which I managed to prove, is there anyway I can use this to answer the question?

Help really appreciated. Thankyou !