if alpha and beta are the roots of the polynomial 2x^2-6x+k=0 and 2alpha + 5 beta = 9
gurdeenkaur31:
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I too don't know if anyone who knows it please let me know
Sorry mate I couldn't help you
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2x2+6x+k=2(x−α)(x−β)=2x2−2(α+β)+2αβ2x2+6x+k=2(x−α)(x−β)=2x2−2(α+β)+2αβ
α+β=−3α+β=−3
αβ=k/2αβ=k/2
αβ+βα=α2+β2αβ=(α+β)2−2αβαβ=(α+β)2αβ−2=18k−2αβ+βα=α2+β2αβ=(α+β)2−2αβαβ=(α+β)2αβ−2=18k−2
For k<0k<0 this increases as k→−∞.k→−∞. αβ+βααβ+βαnever reaches its least upper bound aka supremum of negative two.
α+β=−3α+β=−3
αβ=k/2αβ=k/2
αβ+βα=α2+β2αβ=(α+β)2−2αβαβ=(α+β)2αβ−2=18k−2αβ+βα=α2+β2αβ=(α+β)2−2αβαβ=(α+β)2αβ−2=18k−2
For k<0k<0 this increases as k→−∞.k→−∞. αβ+βααβ+βαnever reaches its least upper bound aka supremum of negative two.
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