Question

If $x^2+3x+5=0$ and $a{x}^2+bx+c=0$ have a root in common and a, b, c $ϵ$ N, then minimum value of a + b + c =

• A. 6
• B. 9
• C. 1
• D. 8

Answer 1

The correct option is B

9

Roots of $x^2+3x+5=0$ are complex.
$\therefore \frac{a}{1}=\frac{b}{3}=\frac{c}{5}=\lambda \Rightarrow \begin{array}{c}a=3\lambda \\ b=3\lambda \\ c=5\lambda \end{array}\Rightarrow a+b+c=9\lambda$
$\therefore$ Min value of a + b + c = 9