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

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Solution

We have,
$(a + 1) x^{2} + (2 a + 3) x + (3 a + 4) = 0$

sum of roots $= \frac{c o n s t a n t t e r m o f x}{c o e f f i e n t o f x^{2}}$

$\Rightarrow$ $\frac{- (2 a + 3)}{a + 1} = - 1$

$\Rightarrow$ $= \frac{2 a + 3}{a + 1} = 1$

$\Rightarrow$ $2 a + 3 = a + 1$

$\Rightarrow$ $a = - 2$

Products of root $= \frac{c o n s t a n t t e r m}{c o e f f i e n t o f x^{2}}$ $= \frac{3 a + 4}{a + 1}$

substitute the value $a$ in above equation

$= \frac{3 (- 2) + 4}{(- 2) + 1}$

$= \frac{- 6 + 4}{- 1}$

$A n s w e r = 2$

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