MathDB

Let

a,b

and

c

real numbers such that the equation ax^2\plus{}bx\plus{}c\equal{}0 has two distinct real solutions

p_1,p_2

and the equation cx^2\plus{}bx\plus{}a\equal{}0 has two distinct real solutions

q_1,q_2

. We know that the numbers

p_1,q_1,p_2,q_2

in that order, form an arithmetic progression. Show that a\plus{}c\equal{}0.

Problem Statement