Number of possible value(s) of integer 'a for which the quadratic equation x2 + ax +16 =0 has integral roots, is

For integral roots discriminant should be a perfect square. ∴ a2−64=λ2,whereλ∈Z ⇒ a2−λ2=64 ⇒ (a+λ)(a−λ)=1×64=2×32=4×16=8×8Since 1 and 64 as factors is not possible. The other possible factors are listed below: α−λ:2−24−48−8α+λ:32−3216−168−8a:17−1710−108−8Hence, a can take 6 integral values.