Which quantity is used to determine the nature of the roots of the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\)?

Correct answer: Discriminant: \(D=b^2-4ac\)

The nature of the roots of a quadratic equation is determined by its discriminant, \(D=b^2-4ac\). If \(D>0\), the roots are real and distinct; if \(D=0\), the roots are real and equal; and if \(D<0\), there are no real roots. Therefore, the discriminant is the correct quantity. Exam tip: first write the equation in standard form and identify \(a\), \(b\), and \(c\) before calculating \(D\).