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If α, β are the roots of ax 2 +bx+c=0 then, the value of α 2 /β 2 + β 2 /α 2 is



If  α, β are the roots of ax2+bx+c=0 then, the value of α22 + β22 is


Grade:Upto college level

2 Answers

jitender lakhanpal
62 Points
7 years ago

 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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vijay
37 Points
7 years ago


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