PQ Formula

linear-algebra

Definition

PQ Formula

The PQ formula is a formula used to find the roots of a quadratic equation:

$$a{x}^2+bx+c=0$$

where a, b, c are coefficients and x is the variable.

The formula is given by:

$$x_{1,2}=-\frac{a}{2}\pm \sqrt{{\left(\frac{a}{2}\right)}^2-b}$$

Derivation

todo

Discriminant

The dicriminant of a quadratic equation defines the number of solutions of a quadratic function.

$$D=b^2-4ac$$

• $D\ge 0⟹$ has two distinct real roots
• $D=0⟹$ has one real root
• $D<0⟹$ has no real roots