What is the discriminant? 

The discriminant in A level maths is a key concept used to determine the nature of the roots of a quadratic equation. It is calculated using the formula b^2 – 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0. The discriminant provides valuable information about the nature of the roots of the equation. For example, if the discriminant is positive, then the equation has two distinct real roots. If the discriminant is zero, then the equation has one real root. If the discriminant is negative, then the equation has no real roots, but instead has two complex roots.

To illustrate the use of the discriminant, consider the quadratic equation x^2 – 4x + 4 = 0. By using the discriminant formula, we can calculate that the discriminant is (-4)^2 – 4*1*4 = 0. Since the discriminant is zero, this means that the equation has one real root. In contrast, if we take the equation x^2 – 6x + 9 = 0, the discriminant is (-6)^2 – 4*1*9 = 0. In this case, the discriminant is positive, indicating that the equation has two distinct real roots.

Furthermore, if we consider the equation x^2 + 2x + 5 = 0, the discriminant is 2^2 – 4*1*5 = -16. With a negative discriminant, we can conclude that this equation has no real roots, but instead has two complex roots. Therefore, the discriminant serves as a powerful tool in A level maths to determine the nature of the roots of a quadratic equation, providing valuable insights into the behaviour of the equation’s solutions.

Get the best grades with structured A Level Maths Easter Revision