Q. If the product of the roots of the equation $(a + 1)x^{2} + (2a + 3)x + (3a + 4) = 0$ is 2, then the sum of roots is
A) 1
B) $- 1$
C) 2
D) $- 2$
Explanation
(b)
We have,
$(a + 1)x^{2} + (2a + 3)x + (3a + 4) = 0$
Let $\alpha\ and\ \beta$ be the roots of the equation.
According to the given condition
$\alpha\beta = 2$
$\Rightarrow \ \frac{3a + 4}{a + 1} = 2$
$\Rightarrow 3a + 4 = 2a + 2$
$\Rightarrow \ a = - 2$
Also, $\alpha + \beta = - \frac{2a + 3}{a + 1} = - \frac{- 4 + 3}{- 2 + 1} = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.