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

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

Complex Numbers and Quadratic Equations

Solution:

It is given that: $\alpha \beta=2 $
$\Rightarrow \frac{3 a+4}{a+1}=2$
$\Rightarrow 3 a+4=2 a+2$
$ \Rightarrow a=-2$
Also, $\alpha+\beta=-\frac{2 a+3}{a+1}$
Putting this value of a, we get sum of roots
$=-\frac{2 a+3}{a+1}=-\frac{-4+3}{-2+1}=-1$