If $- \frac{1}{2}$ is a zero of polynomial $p (x) = 2 x^{2} - 5 x - k$ then find the value of $k$ .

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Solution

$p (x) = 2 x^{2} - 5 x - k$

$p (\frac{- 1}{2}) = 2 (\frac{1}{4}) - 5 (\frac{- 1}{2}) - k = 0$

$\Rightarrow \frac{1}{2} + \frac{5}{2} = k$

$\Rightarrow k = 3$

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