What is the reciprocal sum of the roots for the equation $(x + 2) (2 x - 1)$ ?

\frac{1}{- 3}

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\frac{- 2}{- 3}

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\frac{2}{3}

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\frac{2}{- 3}

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Solution

The correct option is D $\frac{2}{- 3}$
The general form of complete quadratic equation is $a x^{2} + b x + c = 0$
$(x + 2) (2 x - 1) = 0$
$2 x^{2} - x + 4 x - 2 = 0$
$2 x^{2} + 3 x - 2 = 0$
Where, sum of the roots $=$ $\frac{- b}{a}$
Here, the given equation is $2 x^{2} + 3 x - 2 = 0$
So, the value of $b = 3, a = 2$
Sum of the roots $=$ $\frac{- 3}{2}$
Reciprocal of the sum $=$ $\frac{2}{- 3}$

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