roots

first of all toh .. your question has a mistake..
inthe first eqn, the 'c' will be 'q'.
so,

in x^2+px+q=0 , α+β=-p, αβ=q.
in x^2-rx+s=0 , α⁴+β⁴=r, α⁴β⁴=s.

so in the eqn x^2-4qx+2qr-r=0 , let roots be m1 n m2.

m1+m2 = 4q
m1m2 = r(2q-1)

now represent q n r in terms of α,β...

i din solve fully ,, but u will get it this way...