# Quadratic Equation

Quadratic equation is a second order polynomial with 3 coefficients – *a*, *b*, *c*.

The quadratic equation is given by:

*ax*^{2 }+* bx *+* c* = 0

The solution to the quadratic equation is given by 2 numbers x_{1} and x_{2}.

We can change the quadratic equation to the form of:

(*x *–* x*_{1})(*x *–* x*_{2}) = 0

### Quadratic Formula

The solution to the quadratic equation is given by the quadratic formula:

The expression inside the square root is called *discriminant* and is denoted by Δ:

Δ = *b*^{2} – 4*ac*

The quadratic formula with discriminant notation:

This expression is important because it can tell us about the solution:

When Δ>0, there are 2 real roots x_{1}=(-b+√Δ)/(2a) and x_{2}=(-b-√Δ)/(2a)_{.}

When Δ=0, there is one root x_{1}=x_{2}=-b/(2a)_{.}

When Δ<0, there are no real roots, there are 2 complex roots x_{1}=(-b+i√-Δ)/(2a) and x_{2}=(-b-i√-Δ)/(2a)_{.}