Quadratic Equation

A polynomial equation of degree two is called a quadratic equation.

Standard form of quadratic equation

ax² + bx + c = 0 , where a ≠ 0

Roots of Quadratic Equation

Roots of the equation ax² + bx + c = 0

x =

− b ± b² − 4ac 2a

There can be 2 values of x: α, β

α =

− b + b² − 4ac 2a

β =

− b − b² − 4ac 2a

α, β: roots of the equation

Sum of Roots

α + β = − b a

Product of Roots

α × β = c a

Discriminant of Quadratic Equation ( Δ )

The value of (b² − 4ac) is known as the discriminant of the quadratic equation ax² + bx + c = 0.

Δ = b² − 4ac

Discrimination of roots of a quadratic equation

If Δ > 0	: Roots are distinct and real
If Δ = 0	: Roots are equal and real
If Δ < 0	: Roots are distinct and complex