If α, β are the roots of ax²+bx+c=0 then, the value of α²/β² + β²/α² is

 α+β= -b/a ------1  
 α β= c/a -------2    given

 (α^4+β^4)/( α β)^4       sum of roots
(α^4+β^4) = {(α+β)^2-2α β }^2-2 (α β)^2} -----by algebraic identities

now put the equations 1 and 2 in above expression

product of roots = 1

we know the sum and product we can easily form the equation

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