If the sum of the roots of the equation $(a + 1) x^{2} + (2 a + 3) x + (3 a + 4) = 0$ is $- 1$ , then the product of the roots is

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Solution

Let $p, q$ are the roots of the equation $(a + 1) x^{2} + (2 a + 3) x + (3 a + 4) = 0$
Then
$p + q = - 1 \Rightarrow - \frac{2 a + 3}{a + 1} = - 1$
$\Rightarrow a = - 2$
Now, product of the roots is $(3 a + 4) / (a + 1) = (- 6 + 4) (- 2 + 1) = 2$

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