Question 164
Do there exist real numbers $a$, $b$, $c$, $d$ such that the conditions:
a) the equation $ax^2 + bdx + c = 0$ has distinct real roots $x_1, x_2$
b) the equation $bx^2 + cdx + a = 0$ has distinct real roots $x_2, x_3$
c) the equation $cx^2 + adx + b = 0$ has distinct real roots $x_3, x_1$
hold simultaneously?
a) the equation $ax^2 + bdx + c = 0$ has distinct real roots $x_1, x_2$
b) the equation $bx^2 + cdx + a = 0$ has distinct real roots $x_2, x_3$
c) the equation $cx^2 + adx + b = 0$ has distinct real roots $x_3, x_1$
hold simultaneously?