Question 162
Let $a$, $b$, $c$ be different real numbers none of which is zero. Consider quadratic equations:
$$
ax^2 + bx + c = 0, \quad bx^2 + cx + a = 0, \quad cx^2 + ax + b = 0.
$$
If $\frac{c}{a}$ is a root of the first equation, prove that all three of them have a common root. What is the product of the other roots of those equations (different from the common root)?
$$
ax^2 + bx + c = 0, \quad bx^2 + cx + a = 0, \quad cx^2 + ax + b = 0.
$$
If $\frac{c}{a}$ is a root of the first equation, prove that all three of them have a common root. What is the product of the other roots of those equations (different from the common root)?