Question

If the equations $x^2+2x+3=0anda{x}^2+bx+c=0$ , a , b , c $\hat{I}$ R , have a common root, then a: b: c is

• A. 1:2:3
• B. 3:2:1
• C. 1:3:2
• D. 3:1:2

Answer 1

The correct option is A

1:2:3

$x^2+2x+3=0$ ....... (i)

$a{x}^2+bx+c=0$ ......... (ii)

Since equation (i) has imaginary roots

So equation (ii) will also have both roots same as (i) , Thus

$\frac{a}{1}=\frac{b}{2}=\frac{c}{3}\Rightarrow a=\lambda ,b=2\lambda ,c=3\lambda$

Hence 1:2:3