Quadratic equation is a second order polynomial with 3 coefficients – a, b, c.
The quadratic equation is given by:
ax2 + bx + c = 0
The solution to the quadratic equation is given by 2 numbers x1 and x2.
We can change the quadratic equation to the form of:
(x – x1)(x – x2) = 0
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 = b2 – 4ac
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 x1=(-b+√Δ)/(2a) and x2=(-b-√Δ)/(2a).
When Δ=0, there is one root x1=x2=-b/(2a).
When Δ<0, there are no real roots, there are 2 complex roots x1=(-b+i√-Δ)/(2a) and x2=(-b-i√-Δ)/(2a).