Quadratic functions

Question

Which of the following conditions must be true for the parabola 

y=ax²+c to have exactly two x? 

Answer 1

I assume you mean which conditions must be true to have 2 real roots.

 

ax² + bx + c = 0

 

x = (1/2a)[-b ± √(b² - 4ac)]

 

b = 0 in this problem, so

 

x = ±√(-4ac) / 2a

 

-4ac must be positive, so either a < 0 or c < 0, but not both.  Also, neither a or c can be zero.  (If either is zero, you have only 1 root).