First slide

Theory of equations

Question

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

Moderate

A

$1$
B

$- 1$
C

$2$
D

$- 2$

Solution

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

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