No real zeros in quadratic functions y=x^2+bx+c

Question

Consider a family of quadratic functions y=x^2+bx+c where b and c are integers between 1 and 8 inclusive. How many of these families have no real zeros?

Answer 1

y=x²+bx+c

 

no real zeros if Discriminant b² - 4c < 0    ("a=1")

 

b² < 4c

 

Now you can play around with various c values, e.g. if c = 1, b² < 4 means b can only equal 1.

Proceed with c=2; b² < 8 means b can only be 1 or 2.

Continue the study, and add up all possibilities to give the total requested.