if alpha and beta are the zeroes of the polynomial f(x)=x^2-6x+k, then find the value of k, such that apha^2+ beta^2= 40
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α+β = -b/a = -(-6)/1 =6
αβ =c/a =k/1 =k
now its given that
α²+β² =40
(α+β)² - 2αβ =40
substituting the values we get ,
(6)² -2k =40
36-2k =40
2k = 4
k =2
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