A-Level MathsDiscriminants

The discriminant of a quadratic equation will tell you how many roots the quadratic equation has.

Solutions of a quadratic equation are known as roots; they can be seen on the graph of a quadratic where the graph crosses the x-axis. Recall that the general quadratic equation: ax^2+bx+c=0, can have two distinct roots, one repeated roots or no roots at all (unless you are working with complex numbers).

The discriminant can tell you how many roots a quadratic equation will have without having to actually find them.

For the quadratic equation ax^2+bx+c=0, the discriminant is given by b^2-4ac.

  • If b^2-4ac \hspace{2pt}\textgreater\hspace{2pt} 0, the equation has two distinct roots.
  • If b^2-4ac = 0, the equation has one repeated root.
  • If b^2-4ac\hspace{2pt}\textless\hspace{2pt}0, the equation has no roots.

Example 1

Given that the quadratic equation kx^2-4x+2 has equal roots, find the value of k.

Example 2

A quadratic has equation y=px^2+3px-5.

  1. Calculate the discriminant of the quadratic.
  2. Given that the quadratic has two distinct roots, find the possible values of p.