Question

The equations $x^2+3x+5=0$ and $a{x}^2+bx+c=0$ have a common root. lf $a,b,c\in N$, then the least possible value of $a+b+c$ is equal to

• A. $3$
• B. $6$
• C. $9$
• D. $12$

Answer 1

Answer: (C)

$9$

$\frac{{\alpha }^2}{3c-b5}=\frac{\alpha }{5a-c}=\frac{-1}{3-b}$
$x^2+3x+5=0$ and $a{x}^2+bx+c=0$ have a common
root $\Rightarrow \frac{a}{1}=\frac{b}{3}=\frac{c}{5}$
$\therefore$ minimum value$=1+3+5=9$ as $a,b,c\in N.$