COMC 2022 C Problem 1

a. Find all integer values of a such that equation x^{2}+a x+1=0 does not have real solutions in x.

b. Find all pairs of integers (a, b) such that both equations

x^{2}+a x+b=0 \quad \text { and } \quad x^{2}+b x+a=0

have no real solutions in x.

c. How many ordered pairs (a, b) of positive integers satisfying a \leq 8 and b \leq 8 are there, such that each of the equations

x^{2}+a x+b=0 \quad \text { and } \quad x^{2}+b x+a=0

has two unique real solutions in x?