If the equation x2 + 2x + 3 = 0 and ax2 + bx + c = 0, a, b, c \in R, have a common root, then a : b : c is :

Engineering

Mathematics

Condition for Common Roots

Question

If the equation x² + 2x + 3 = 0 and ax² + bx + c = 0, a, b, c $\in$ R, have a common root, then a : b : c is :

1 : 2 : 3

1 : 3 : 2

3 : 1 : 2

3 : 2 : 1

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For x² + 2x + 3 = 0, D < 0

$\Rightarrow$ both equations has both roots common.

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