SOLUTION: if α and β are zeroes of 3x^2+8x+2 ,find value of α^2+ß^2 1) a^3+ß^3 2) a^4+ß^4 3) α^2+ß^2

The zeros  and  of

 

are also the zeros of



which is the original divided through by 3, the coefficient of .
Known facts about the relationships between the coefficients and the 
zeros of a monic polynomial tell us that:



and



Since:



then multiplying both sides by -1:



Squaring both sides:





and now since , we substitute  for :





So 





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1) 

We can find that by factoring the sum of two cubes.  We already
have values for  and .



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2) 

We have 



Squaring both sides gives:





And since ,













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You stop there but we could show that 



and 



and



and



and as far as we like.

Edwin