If \(f(x)=x^2+ax\) and \(g(x)=x^2-ax\), and their product satisfies \((fg)(1)=0\), what are the possible real values of \(a\)?

Correct answer: \(a=\pm 1\)

For the product of functions, \((fg)(1)=f(1)g(1)\). Here, \(f(1)=1+a\) and \(g(1)=1-a\), so \((1+a)(1-a)=0\). By the zero-product property, \(a=-1\) or \(a=1\), hence \(a=\pm1\). Option B is incorrect because substituting \(a=0\) gives a product equal to \(1\). Exam tip: Evaluate the functions at the specified point first, then apply the zero-product property.