Question

If $x^2+3x+5=0$ and $a{x}^2+bx+c=0$ have a common root and $a,b,cϵN$, then minimum value of $a+b+c$ is equal to:

• A. $0$
• B. $1$
• C. $3$
• D. $9$

Answer 1

Answer: (D)

$9$

Consider, $x^2+3x+5=0$

$a=1,b=3,c=5$

Let $p,q$ be the two roots. Now, by Vieta's formulas,

$p+q=-3=-ba$ and $pq=5=ca$

Therefore, $b=3a,c=5a$. Hence, $a+b+c=a+3a+5a=9a$. But given that $a,b,cϵN$.

$\therefore$ The minimum value of $a+b+c=9$