If a, ß are the roots of the polynomial f(x) = 2x2 + 5x + k satisfying the relation o? +B+ QB = 27, then find the value of k for this to be possible.

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Ans: 2 ( alpha+beta=-frac{5}{2} ) and ( alpha beta=frac{k}{2} ) ( alpha^{2}+beta^{2}+alpha beta=frac{21}{4} ) ( Rightarrow(alpha+beta)^{2}-alpha beta=frac{21}{4} Rightarrow frac{25}{4}-frac{k}{2}=frac{21}{4} Rightarrow k=2 )

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