Number of possible value (s) 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, where λ∈Z⇒ a2−λ2=64⇒ (a+λ)(a−λ)=1×64=2×32=4×16=8×8Since 1 and 6 factors not possible. The other possible factors are listed below:α−λ:    2        −2    4      −4    8    −8α+λ:    32    −32    16    −16    8    −8a:          17    −17    10    −10    8    −8Hence. a can take 6 integral values