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  4. If the sum of the roots of the equation (a+1)x2+(2a+3)x+(3a+4)=0, where a ≠ -1 , is -1, then the product of the roots is

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Q. If the sum of the roots of the equation $\left(a+1\right)x^{2}+\left(2a+3\right)x+\left(3a+4\right)=0,$ where a $\ne$ $-1$ , is $-1$, then the product of the roots is

KEAMKEAM 2013Complex Numbers and Quadratic Equations

Solution:

Given equation is,
$(a+1) x^{2}+(2 a+3) x+(3 a+4)=0$ ;
$ a \neq-1$
and sum of the roots $=-1$
$\Rightarrow \, -\frac{(2 a+3)}{(a+1)}=-1$
$\Rightarrow \, 2 a+3=a+1$
$ \Rightarrow \,a=-2$
$ \therefore $ Product of the roots $=\frac{3 a+4}{a+1}=\frac{3(-2)+4}{-2+1} $
$(\because a=-2) $
$= \frac{-6+4}{-1}=2 $