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ll one zero of rhe polynomial 2x2 +3x+kis 1/2, find the value of k and the other zero.

$L e t t h e p o l y n o m i a l f (x) = 2 x^{2} + 3 x + k G i v e n, o n e z e r o o f t h e p o l y n o m i a l f (x) i s \frac{1}{2} . L e t t h e a n o t h e r z e r o b e α . T h u s, α + \frac{1}{2} = - \frac{c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}} = \frac{- 3}{2} \Rightarrow α = - \frac{3}{2} - \frac{1}{2} = \frac{- 3 - 1}{2} = - 2 A n d, α \times \frac{1}{2} = \frac{c o n s \tan t t e r m}{c o e f f i c i e n t o f x^{2}} = \frac{k}{2} \Rightarrow (- 2) \times \frac{1}{2} = \frac{k}{2} \Rightarrow k = - 2 H e n c e, o t h e r z e r o i s - 2 a n d v a l u e o f k i s - 2.$

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