If the sum and product of the zeroes of \(p(x)=x^2-ax+a\) are equal and \(a\ne0\), what can be the value of \(a\)?

Correct answer: Any non-zero real number

For a quadratic polynomial \(x^2+bx+c\), the sum of the zeroes is \(-b\) and their product is \(c\). Here, \(b=-a\) and \(c=a\), so both the sum and product are \(a\). Hence the condition is automatically satisfied for every non-zero real value of \(a\). The values 1, −1, and 2 are only particular examples, not the complete answer. Exam tip: compare \(-b\) and \(c\) directly when using the relationships between zeroes and coefficients.