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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Solution:
- Given equations are $x^{2}+2 x+3=0$
and
$$ a x^{2}+b x+c=0 $$
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 $1: 2: 3$.
