Question

Consider a quadratic polynomial f (x) = ax^2 + x + c such that ac >1/4 and it's graph completely lies below x-axis
1) a<0, c >0
2) a<0, c<0
3) a>0, c>0
4) a>0, c<0

Answer 1

Answer:

2) a<0, c<0

Step-by-step explanation:

Since the graph is below the x-axis, it follows that a < 0.  So the answer is either (1) or (2).

Since ac > 1/4, in particular, this means that the product ac is positive.  So since a is negative, it follows that c is negative, too.  So the answer is (2)... both a<0 and c<0.