Final answer:
Coefficients b and c in the equation x^2 + bx + c = 0 are the roots of the equation, following which b = 0 and c can be any non-zero number.
Step-by-step explanation:
The question indicates that the coefficients b and c in the equation x^2 + bx + c = 0 are in fact the roots of the equation, with the condition that c ≠ 0. Since any quadratic equation of the form x^2 + bx + c = 0 has its roots sum and product represented by -b/a and c/a respectively, and since the leading coefficient a = 1 in this case, the roots of the equation, which are also the coefficients b and c, can be derived. Thus, b = -b, which implies that b = 0, and c = c. Since c ≠ 0 by the question's condition, c can be any non-zero number.