Question No.
Solution:
Given equation has four roots √e,√f,√g,√h
( I will refer to alpha, beta ,gamma,delta as e,f,g,h )
Now we try to find out the equation that has the roots e,f,g,h. (
This technique is called transformation.)
x^4+fx^2+gx+h=0
x^4+fx^2+h=(-gx)
Squaring and simplifying we get
x^8+2fx^6+(f^2+2h)x^4+(2fh-c^2)x^2+h^2=0
Put x^2=y , we get
y^4+2fy^3+(f^2+2h)y^2+(2fh-g^2)y+h^2=0
The above equation has the roots e,f,g,h.
64efgh-[4sum(ef)-(sum(e))^2]^2
=64h^2-[4(f^2+2h)_(2f)^2]^2
=0