**Discriminant** | **Real roots** Delta=b2-4ac>0 | Two distinct Delta=0 | One repeated Delta<0 | None Delta>0 Delta=0 Delta<0 First check a 0. If a parameter makes the quadratic coefficient zero, examine that resulting equation separately. Example For x2+kx+9=0, two distinct real roots require k2-36>0, giving k<-6 or k>6. Equal roots occur when k=+-6.

First check \(a\ne0\). If a parameter makes the quadratic coefficient zero, examine that resulting equation separately.

For \(x^2+kx+9=0\), two distinct real roots require \(k^2-36>0\), giving \(k<-6\) or \(k>6\). Equal roots occur when \(k=\pm6\).

Quadratic Functions, Equations and Inequalities

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

The discriminant

The discriminant