The root(s) of the quadratic equation $2 x^{2} + 5 x - 12 = 0$ is/are

\frac{3}{2}

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- 4

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\frac{2}{3}

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4

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Solution

The correct option is B $- 4$
Given, $2 x^{2} + 5 x - 12 = 0$
Let $α, β$ be the roots of the equation $a x^{2} + b x + c = 0$
Then $α = \frac{- b + \sqrt{D}}{2 a}$

$β = \frac{- b - \sqrt{D}}{2 a}$
$D = b^{2} - 4 a c$ is the discriminant of the equation.
Here, $D = 5^{2} - 4 (2) (- 12) = 121$
$\Rightarrow \sqrt{D} = 11$
$α = \frac{- 5 + 11}{2 \times 2} = \frac{3}{2}$
$β = \frac{- 5 - 11}{2 \times 2} = - 4$

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