If, for real constants p and q, the expression \(x^2+px+q\) can be written as the perfect square of a binomial involving \(x\) and a constant, which relation between \(p\) and \(q\) is necessary?

Correct answer: \(q=\frac{p^2}{4}\)

For a perfect square, \(x^2+px+q=(x+\frac p2)^2\). Squaring gives the constant term \(\frac{p^2}{4}\), so \(q=\frac{p^2}{4}\). The choice \(q=p^2\) wrongly ignores halving the coefficient of \(x\). Exam tip: halve the middle coefficient, then square it.