Question

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

• A. 3
• B. 9
• C. 6
• D. 12

Answer 1

The correct option is B

9

$x^2+3x+5=0$ has imaginary roots which are complex conjugate.

$\therefore$ $x^2+3x+5=0,a{x}^2+bx+c$ have both roots in common.

$\therefore$ $\frac{a}{1}=\frac{b}{3}=\frac{c}{5}=\lambda$

$\Rightarrow a+b+c=9\lambda ,a,b,cϵN\Rightarrow$ \lambda \in N \)

$\Rightarrow$ min. ( a+ b +c ) = 9.