Question 8
(NET 4) Determine whether there exist distinct real numbers $a,b,c,t$ for which:
(i) the equation $ax^2+btx+c=0$ has two distinct real roots $x_1,x_2$,
(ii) the equation $bx^2+ctx+a=0$ has two distinct real roots $x_2,x_3$,
(iii) the equation $cx^2+atx+b=0$ has two distinct real roots $x_3,x_1$.
(i) the equation $ax^2+btx+c=0$ has two distinct real roots $x_1,x_2$,
(ii) the equation $bx^2+ctx+a=0$ has two distinct real roots $x_2,x_3$,
(iii) the equation $cx^2+atx+b=0$ has two distinct real roots $x_3,x_1$.