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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

1. 1: 2: 3
2. 3: 2: 1
3. 1: 3: 2
4. 3: 1: 2

Correct answer: 1: 2: 3

Solution

The equations share a common root, which implies that the coefficients of the second equation can be expressed in terms of the coefficients of the first equation. By substituting the common root into both equations and simplifying, we find that the ratio of the coefficients a, b, and c must be 1:2:3 to maintain the equality.

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