Question:
If the equations $x^2+2x+3=0$ and $ax^2+bx+c=0, a, b, c \in R$ have a common root, then $a : b : c$ is
If the equations $x^2+2x+3=0$ and $ax^2+bx+c=0, a, b, c \in R$ have a common root, then $a : b : c$ is
Updated On: Mar 25, 2026
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The Correct Option is A
Solution and Explanation
Given equations are $x^2+2x+3=0 ...(i)$
and $ ax^2+bx+c=0 ...(ii)$
Since, E (i) has imaginary roots, so E (ii) will also
have both roots same as E (i).
Thus,$ \frac{a}{1}=\frac{b}{2}=\frac{c}{3}$
Hence, a : b : c is 1 : 2 : 3.
and $ ax^2+bx+c=0 ...(ii)$
Since, E (i) has imaginary roots, so E (ii) will also
have both roots same as E (i).
Thus,$ \frac{a}{1}=\frac{b}{2}=\frac{c}{3}$
Hence, a : b : c is 1 : 2 : 3.
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
