Question

If $\alpha ,\beta$ are roots of equation $x^2+6x+\lambda =0$ and $3\alpha +2\beta =-20$, then $\lambda$ is equal to

• A. $16$
• B. $-8$
• C. $-16$
• D. $8$

Answer 1

The correct option is D $8$

$\{x^2+6x-\lambda =0\}$

$\alpha$ & $\beta$ are roots of this $e{q}^n$

$\Rightarrow \alpha +\beta =\frac{-6}{1}...\left(1\right)\alpha \beta =\lambda$

and $3\alpha +2\beta =-20...\left(2\right)$

$3(\alpha +\beta )=-6\times \mathrm{3...}\left(3\right)$ (Multiplying (1) $\times$ 3)

on subtracting (2) & (3), we get

$3\alpha +2\beta =-20$

$-3\alpha +3\beta =-18$

_______________

$-\beta =-2$ ,

$\beta =-2$

$\alpha =-6-\beta =-6-(-2)=-6+2$

$=-4$

$\alpha =-4$

$\therefore \lambda =\alpha \beta$

$=(-4)(-2)=8$

$\lambda =8$ option D is correct.