Theory of Equations 2 Question 1

2. If the equations $x^{2}+2 x+3=0$ and $a x^{2}+b x+c=0$, $a, b, c \in R$ have a common root, then $a: b: c$ is

(a) $1: 2: 3$

(b) $3: 2: 1$

(c) $1: 3: 2$

(d) $3: 1: 2$

(2013 Main)

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Answer:

Correct Answer: 2. (a)

Solution:

  1. Given equations are $x^{2}+2 x+3=0$

and $ \quad a x^{2}+b x+c=0 $

Since, Eq. (i) has imaginary roots, so Eq. (ii) will also have both roots same as Eq. (i).

Thus, $\quad \frac{a}{1}=\frac{b}{2}=\frac{c}{3}$

Hence, $a: b: c$ is $1: 2: 3$.



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