The quadratic equation x2+ax+b=0 has real roots if D=a2−4b≥0 ⇒a2≥4b when b=1,a2≥4 The possible set of values of a are 2, 3 and 4. When b=2,a2≥8 The possible set of values of a are 3 and 4. When b=3,a2≥12 The possible set of value of a is 4. When b=4,a2≥16 The possible set of value of a is 4. Thus, the possible pairs of values of a and b are 7.