If \(\alpha\) and \(\beta\) are the zeroes of \(x^2-8x+k\) and \(\alpha-\beta=2\), what is the value of \(k\)?

Correct answer: 15

By Vieta’s formulas, \(\alpha+\beta=8\), since the coefficient of \(x\) is \(-8\). We are also given that \(\alpha-\beta=2\). Adding the two equations gives \(2\alpha=10\), so \(\alpha=5\) and \(\beta=3\). For \(x^2-8x+k\), the product of the zeroes is \(\alpha\beta=k\). Hence, \(k=5\times3=15\). Exam tip: In a monic quadratic \(x^2+bx+c\), the product of the zeroes is \(c\), so 16 is not correct.