If one root of ${2 x}^{2} + p x + 3 = 0$ be $3$ . Find the value of $p$ .

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Solution

The correct option is A $- 7$
Given equation is:
${2 x}^{2} + p x + 3 = 0$
$∵$ one root $= 3$ .
Let other root $=$ $β$
$\Rightarrow 3 β = \frac{3}{2} \Rightarrow β = \frac{1}{2}$
$\Rightarrow α + β = \frac{- b}{a} = \frac{- p}{2}$
$\Rightarrow 3 + \frac{1}{2} = \frac{- p}{2}$
$\Rightarrow \frac{7}{2} = \frac{- p}{2}$
$\Rightarrow e p = - 7$

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