Given the equation ax2 + bx + c = 0, describe a set of conditions such that the equation has two solutions that are opposite values.

Question

A. The equation must be the difference of squares.
B. The equation 0 = ax2 + bx + c must have b = 0 and ac < 0.
C. both of the above
D. none of the above

Answer 1

a(x-p)(x+p)=ax^2+bx+c

ax^2-ap^2=ax^2+bx+c

b=0, c=-ap^2

p^2=-c/a --> ac<0  (which is th same as -c/a=-ac/a^2).

 

B. b=0 and ac<0