SATHEE: Theory of Equations 2 Question 1

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) $3 : 2 : 1$

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

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

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Theory of Equations 2 Question 1

2. If the equations x2+2x+3=0 and ax2+bx+c=0, a,b,c∈R have a common root, then a:b:c is

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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